解析几何教程+(廖华奎王宝富)+课后习题

《解析几何教程+(廖华奎王宝富)+课后习题》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。

ᔣᦪ⚪1.11.ᔣḄᔠᓽᔣa,cᡂ(a+b)+c=a+(b+c).ᔣ=a,=஻,=(᝞%&)ᑣ(a+b)+c=(AB+BC)+CD=AC+CD=AD,a+(b+c)=AB+(BC+CD)=AB+Bb=AD,ᦑ(a+b)+c=a+(b+c).2.*a,),c++,ᐳ./0123Ḅ4567589ᡂ
:;<=Ḅᐙ⌕ᩩABa+Z>+c=O.C⌕ឋ*a,b,cḄ4567589ᡂ
:;<=AA5C,ᑣa+b+c=Z^++F=/+F=ᐔ5=0.ᐙᑖឋᔣJK=a,=L,=஺ᵫO0=஺+6+=43+3஺+஺஺=4஺+஺஺=4஺,ᡠQ546஺Rᔠᓽ;ᔣa,b,cḄ4567589᪀ᡂ
:;<=஺

13.;<=Ḅ;T.UQ᪀ᡂ
:;<=஺*;<=A43C;VAB,3C,C4ḄT5ᑖWB(᝞%&)XYZa=AB,b=BC,c=CA,ᑣ᪷\]T^1.1.1,;ᩩT.⊤`ḄᔣᑖWBCD=-(c-b),AE=-(a-c),BF=-(b-a),222ᡠQCD+AE+BF=-(c-b)+-(a-c)+-(b-a)=Oᦑᵫa⚪bc;<=222Ḅ;T.CD,UQ᪀ᡂ
:;<=஺4.ᵨᔣe=+ῪT59.ghOaஹ%jYkO23lmnḄ
o஺᝞%&e=4BC0+ῪT5ᑖWpE,qZᔣr=஺s=Kᑣ=জᔣuv6wᐳ.Yxᔣ,ᡠQyᙠ{ᦪ2>0,|cDC=A,AB,}ᙠᡝ=8+a,=—b+4a,ᵫOEB5஺ḄT5ᡠQ=5+)=’(஺+“+2«—6)=’(1+1)«=(1+4)4FY2222;(1+ಘ=(|Ἐ+2)=(|Ἐ+|DC|).ᦑe=+ῪT59.ghOaஹ%jYkO23lmnḄ
o஺5.⚪1.1.2o

2C⌕ឋ*a,b,cᐳ☢᝞ᐸTᨵ+:Bᐳ.Ḅ᝞B,ᑣa,.ឋ8ᐵa,A,c.ឋ8ᐵ஺}ᙠ*a,A,c++,ᐳ.ᑣᔣcUQᙠ+:ᔣ஺,5aḄhᑖᓽQcp<.VghOa,ḄghV=ᑣyᙠ{ᦪ஻|cc=Xa+p,b,a,Z>,c.ឋ8ᐵ஺ᐙᑖឋ*a,b,c.ឋ8ᐵ,ᑣyᙠ,ᐰpḄᦪJ,&|cᓰ4+¢+&=0஺,£*v0,ᑣᔣcUQ⊤`pᔣa,LḄ.ឋ¤ᔠ¥ᵫᔣḄghV=ᑣ¦⍝ᔣcghOᵫᔣa,L¨©Ḅg☢ᦑa,K,cᐳ☢஺6.*A,5,CB,ᐳ.Ḅ;523¨©
g☢n,ª«qᙠnaḄᐙ⌕ᩩAByᙠ¬
Ḅᦪ¤(1,஻/)|c[OP=AOA+uOB+vOC,...i,(*)[A+//+v=1,ᐸT0B
5஺qᙠA45CᑁḄᐙ⌕ᩩAB(*)6¯120,஻2020x°ᡂ஺C⌕ឋ᝞%`&9±APX²l³´.3cOR஺ᑣᵫ;55,R,Cᐳ.yᙠ¬
Ḅᦪ¤A1,&|cµ=&1+&2XY&+&=1஺ᵫ;54,P,Rᐳ.yᙠ¬
Ḅᦪ¤¶ὡ|c=1|¸+6µXYZ.+Z=lOOBOP=ldA+ldR=ldA+lJidB+lkdC,*2i1xi112=Z,,/z=v=lk,ᵫk^k,ZZḄ¬
ឋ¦⍝Ḅ¬
ឋ,ᑣ222P2OP=AOA+/1OB+vOCYP+஻+i=4+12kl+12k2=O9ᐙᑖឋᵫ¹¦ᩩAᨵOP=WA+juOB+vOC=WA+piOB+(1-2-஻)OC

3=2(04—OC)+஻(஺8—஺஺)+஺஺=A,CA+nCB+,cᑮCP=ACA+"CBᔣ0ᐳ☢ᓽqᙠ4,3,C¨©Ḅg☢a஺᝞PᙠA43CᑁᑣPᙠ.¼ARᑁRᙠ.¼5cᑁOB0Wᓰ½6"2«1ᑣ04஻,y41஺¾¿*ÀᡂY04Á4Â41,ªÃÄ=ÁF+஻ÅÆ5qᙠ

4xᳮcᑮÕ=L5஺ᦑcRO=1AD,RE=-BE.7778.ᵨᔣAABCḄ;ᩩT.³O
5P,XY
5஺ᨵOP=^(OA+OB+OC).*஺,E,qᑖWBVAB,8C,CAḄT5ᑣ³O
5P,9±ACP,CDoᵫA,P,E;5ᐳ.yᙠJ|=JÄ+(1—4)=,«F+(1—×2ᵫ8,P/;5ᐳ.yᙠ/|Ø+(1-1)=1/+(1-1)OBc2112—>11
-k=l-l,-l=l-k,ck=l=-஺ᨵCP=—C8+—C4,ᯠ22333__ττ_____2__Ä=
+—Úᦑ=
ᓽC,P,O;5ᐳ.A45cḄ;ᩩT.³O
5223P஺Û
50,ᵫÄ=4+1FcIJOP-OC=-(dB-OC)+-(OA-OC),3333OBÄ=¯(+µ+Ü).9.ᵨᔣ☢ÝA5COḄÞT59.³O•5P,Y
5஺ᨵOP=1(19A+OB+OC+OD).*☢ÝA5COḄÞ43,4஺,4஺ḄT5ᑖWB3',஺',0',Þ3஺,஺,஺3ḄT5ᑖWBE,JF,G,᝞%&஺ᑣÞT59.p52,C'G,0'E஺

5ArCD'Dᑣá᧕¦⍝ã=ä3*=/åC'D'=-CD=EG,¥V=C'D'GEBgh22V=C'G,O'E8³Y³5Bᔜ.¼ḄT5஺xᳮ3'q,C'Gç8³Oᔜ.¼ḄT5ᦑ5'F,C'G,D'E³O
5P஺ᵫQab¦⍝
50,ᵫPB஺'EḄT5ᨵ0^=-(0^+0£)=-(-0^+-01)+-0€+-08),222222ᓽ=¯(è+஺5+Æ+OD).10.*A(i=1,2,…,஻)B஻V=Ḅ⚔50B2ḄTvuê=0.1=1n2jr2ᐕ*஺=ëêÏE஻V=íḼTvïðñ஺
L☢ᔣaí50ïðò

6AOA+p,OB+vOC=0=>l+஻+v=Oᐸ@o3ABCDḄE+஺)F*G⌕ឋ᝞J+4,3,C@KLᨵM+NᔠP᝞4,5NᔠᑣRS=0,ᡠTUᡂW஺᝞JA,8,CXNᔠᵫY1.1.1Z⍝+A,B,Cᐳ-Ḅᐙ⌕ᩩ234ᙠᦪ\<]^+(1-4)஺_E`=0,a4=%,஻=1—\@=E1,ᑣ;bᐰ78ᨵAOA+(1OB+vOC=0,4+஻+v=A+(l-A)—1=0஺ᐙᑖឋd>I+஻e+vf=0=;l+M+v=0,gIJ4h+஻᝞E(i+஻)j=0,A(OA-OC)+ju(OB-OC)=ACA+pCB=0,ᵫ!4,஻kᐰ78l+஺ḄABឋZ;ᐰ78ᔲᑣvn78஺ᡠod2*0,ᑣh=-4T஻RpR+4,3,Cᐳ-஺q⚪1.21.sDtᙶ᪗wdx(x,y,z),yPᑖzᐵ!xOy|☢x~+Ḅ+Ḅᙶ᪗஺*ᙠtᙶ᪗w+P(x,y,z)ᐵ!xOy☢x~+Ḅ+Ḅᙶ᪗ᑖz32.d|4BC0Ḅ-!+P,d=9h=.ᙠ᪗A;RRy+P,M,NḄᙶ᪗lᔣḄᙶ᪗஺*᝞Bp7P3஺B@+ᡠ⊟=,+R.22

7AM=DM+AD=-DB+AD^-(AB-AD)+AD=-AB+-AD.5555=:⊟=(+R).ᦑᙠ᪗A;ᝅ⃁“+P,M,NḄᙶ᪗ᑖzJ114ஹ55ஹ7¢,5),!?(%*),=MD+DC+CN=-BD+AB--AC56=^(Ab-AB)+AB--(AB+Ai))=—AB+—AD,563030ᡠᔣ£ᙠ᪗A¤Ḅᙶ᪗7ᖽ,>3.da=(1,5,2),5=(0,—3,4),c=(—2,3,—1),,yᑡᔣḄᙶ᪗*(1)2a—b+c*(2)—3a+2b+4c(1)2a-+c=2(1,5,2)-(0,-3,4)+(-2,3,-1)=(0,16,-1).(2)-3a+2b+4c=-3(1,5,2)+2(0,-3,4)+4(-2,3,-1)=(-11,-9,-2).4.ᑨ¬ᑡᔜ®Ḅ¯ᔣa,A,c3ᔲᐳ☢°±ᔲ²c⊤ᡂa,5Ḅ-ឋ®ᔠ°´±⊤ᑣᑏb⊤஺পa=(5,2,1),஻=(-1,4,2),c=(-1,-1,5);(2)a-(6,4,2),஻=(ߟ9,6,3),c=(-3,6,3);(3)a=(1,2,—3),b-(-2,-4,6),c=(1,0,5).*(1)dᓰa+·b+\3c=0,ᓽ&(5,2,1)+k2(—1,4,2)+/(-1,E1,5)=0,ᑣᨵ5k-k—k=0,t23•2%+4¹Eº=0,£»¼®½ᨵ8ᓰ=&=¿=0,ᡠᔣᐳ☢஺kஹ+2k2+5A=0.(2)dka+kb+kc=0,ᓽ&(6,4,2)+¹(E9,6,3)+À3(—3,6,3)=0,ᑣᨵl23

86k]-9k2-33=0,—3kE43=0,2«4kl+6k2+6k3=0,£»¼®Á!ᵫÂᑮ2kl+3k2+3k3=0.2kl+3k2+3k3=0.12kஹ=EEk,,k=EEý⌕ẑ78ᓃ,nÆ78ᡠᔣᐳ☢஺C¹=12ᑣÇ=—,,¹=—2,ᡠc=a+2জᓽc⊤ᡂa,bḄ-ឋ®ᔠ஺2323(3)dk^+kb+kc=^ᓽk(1,2,-3)+k(-2,-4,6)+k(1,0,5)=0,ᑣᨵ23x23ᓰ-2A2+Ë=஺,“Ìk—2k=0,Í2%EÏ2=0,£»¼®Át!2'»¼®ᨵÑ8Ò2,1,0Ô,▲k=0-3%+6kz+5&=0.3ᔣᐳ☢஺ᵫ!·½±78ᦑc±⊤ᡂḄ-ឋ®ᔠ஺5.ᙠAA5C@dO,E35஺Ḅᑖ+(ᵨØ⊟⊤bRÙ஺6.dᙠE|☢nÀCE¯᪗Û஺>4*2À+ὡ.Ò¹,Ô1=1,2,3,ᐳ-ÞᓰJ,1=ßÞxy1=0.22X3%1)F*+ÍÒᜩGÔ,â=1,2,3,ᐳ-Þ=ßÞᨴᨴAR,ᓽ᳝å=2\.æEᱏy3fêXJ2+*2%+*3%E*1%-Xy-*2%=°-32íJl1xy1=0æêᑡxy+xy+xj,-xy-xy-xy=0.ᦑî⚪ᡂ22r2233x3322l£y13W஺7.ᙠA43C@dP,?,Rᑖz3t-AB,3C,CAÀḄ+ð=AP=AJPB,BQ=pQC^CR=vRA.)FP,Q,Rᐳ-Þ=ßÞ44V=-1.)F*᝞BQ

9ᵫ!P,Q,Rᑖz3t-A3,3C,C4ÀḄDPᑖ+ᡠ;ñ_______0᪗ò;/,ᵫ!AP=APB=A,(AB-AP),AP=^PB=^-^AB>AR^AC-RC=AC-vAR,AR=^—AC:1+vBQ^^iQC=BC+CQ,QC=-^—BC,1+4AQ=AC+CQ=AC+-----CB=AC+-^—(AB-AC)=-------AB+-^—AC஺1+ju1+Ml+஻1+"ᡠP,2,Rᙠ᪗ANយḄᙶ᪗ᑖz7x(/—(^஺(ÌE”-òᑘ஺,E)஺᪷ùÀ⚪ḄTUx,2,Rᐳ-Þ=ßÞ1+21+஻1+஻1+v--^ߟ1=0.æêᑡᓽᑮûv=-l.1+஻1+஻0-^ߟ11+v9.()î⚪1.2.1o)F*CD᪗Û஺*”b,4dᔣQ=31஺2஺3)஻=(4஻2஻3).(1)a+b=(ae+ae+ae)+(be+be+be)1l2233ii2233=(a+&)G+(a+b)e+(a+b)e=(a+4·+%ü+â3)•x222333(2)a—b=(ae+ae+ae)—(be+be+be)ii2233i12233

10=3i-+(a-b)e+(a-b)e^=(%—4,·E஻2஺3E஻3)22233(3)Aa=+ae+«e)=kaye+Aae+2ae=(Aa,,Aa,2a)஺2233x223323q⚪1.31.d஻+8+c=0,ý=3,ý=l,|c|=4,yQb+bc+cao*ᵫa+஻+c=0,ý=3,þ=l,|c|=4,0=(a+)+c)(Q+ÿ+c)=|a++,+23b+bC+CQ)=9+1+16+23b+bc+ca),ᡠ஺஻+6C+CQ=-13.2.|a|=3=2,NQb)=—,(3a+2b)(2a—56)஺6(34+28)(24—5/>)=62—102—114b=54-40-1123cos-=14-3373.63.a+367஺5bᚖa—4b7a-2bᚖN3,6)஺a+3b7@—5bᚖ஺4b7a—26ᚖᡠ(a+3b)(7d-5/>)=7|«|2-15|Z>|2+16«6=0,<(a-4)(7a-2஻)=7|a+8-30b=0=2«!"005/(4,஺)='^^=%,ᦑ/(4,)=஺.4.()*+,ᔣ.a,஻/ᨵ|«4-Z>|2+|«-Z>|2=2,+2.1a23ᐳ56)789Ḅ;<,=஺()+>+|a-b=(a+b)(a+b)+(a-b)(a-b)=|«|-+|Z>|"+2aZ>+|a|"+|i>|"-2ab=2\a\"+2|Z>|2.1a'jb3ᐳ5789Ḅ;<,="a8?@ḄABC@DḄEᩩ*G5ḄAH8!C@ḄAH஺5.Iᑡ89"ᔲLMN6)ᳮᵫQRSTUaaVa2.

11(1)\a\a=a2;(2)a(bb)=ab2;(3)a(ab)=a2b;(4)(ab)2=a2b2;(5)(ab)c=a(bc);(6)cQ=c),cwOna(1)┯ef@⊤hᔣ.i@"ᦪ஺(2)LM஻஻=k஺(3)┯ef@ᔣ.2)஺ᐳ5li@ᔣ.a?஺2ᐳ5஺(4)┯e(஺2)2=4222஺0§/3,஻)n“2஻2஺(5)┯ef@ᔣ.(஺p஺cᐳ5li@ᔣ.a(Ac)aᐳ5஺(6)┯eca=cb,cnO=c(a—5)=0=>ca—2ᚖ஺6.()uGDḄᚖAᑖ5w!xywxᑮu⚔xḄ|}~8஺()uGDA45CḄEᩩ@ḄᚖAᑖ5w!xO,D,E,F4&5C,CA@Ḅx,஺x,B,5,C,0,E/xḄᔣ.V஺c,d,ej஺111________ᑣd=—(a+^),e=—S+c),/=—(c+a),AB=b—a,BC=c—b,CA=a—c.222ᵫ!஺D,OE"A3,3CḄᚖAᑖ5ᡠABd=-(b2-a2)=0,BCe=-(c2-b2)=0,a2=c2=b2,ᵫ7ᑮ22/=—c2)=o,6)஺"C4ḄᚖAᑖ5ᓽuGDḄᚖAᑖ5w!x,2ywxᑮu⚔xḄ|}~8஺7.()஻,),c3ᐳ☢᝞ᔣ.ra-O,rb=,rc=0,ᑣr=0஺()Q,஻
C3ᐳ☢ᡠ=xa+y஻+zc஺ᑣrr=r(xẆy)+zc)=xra+yrb+zr஺=0,ᦑr=0஺8.ᵨ;<()¡ay4…£஻%஽¥…஻஻%஺¦஺?…஺஻/"§ᦪᑣᨵ

12&+6+c+M+b+c+…+M+b+cN+஺2"•------ba஻)2+(4+52------b")2+(C]+C2H-----^C஻)28©ᡂ«Ḅᐙᑖ⌕ᩩ¯"a,:b:c=a:b:c=-=a:b:cytt222nnn“1%"2%…%"”°,%2%…%)”%1,%2,…,C“ᑖ±ᔣ²஺()ᙠGᙶ᪗¶Iᔣ.%=(%,஻.,q),i=1,2,…,஻.ᑣᵫuG3891%+4+…+%141ali+|4|+…+,¸¹y8©ᡂ«Ḅᩩ¯"ᔣ.«,=(4%4,4)/=1,2,…஻ᔣºᙶ᪗»ᐭ½ᨵJa+*+c+M+b+c+.+¾+d+஺%¿J("l+஻2"*------baj+(4+ஹ2------*■஻஻)2+(஺1+஺2------^C஻)28©ᡂ«Ḅᐙᑖ⌕ᩩ¯"᜜545C]=Â55஺2=…=%5256y“1஺2♦“஻"1.)஻01…0”ᑖ±F஺R⚪1.41.஺'⊤hᔣ.஺ᙠᔣ.2஺஺ᚖḄA☢TḄᢗÆᑣᨵax)=a'x)஺()ᵫ!Ç⊤hᔣ.஺ᙠᔣ.Èn0ᚖḄA☢TḄᢗÆ(᝞IÉ)ᑣᵫ2᪀ᡂḄABC@DḄ☢Ë஻᪀ᡂḄÌDḄ☢Ë~8axZsa'xbḄᔣ~l,axb=afxb஺2():(axb)2=a2b2—(ab)2o()(ax))2=a2b2sin2N(a,b),a2b2-(ab)2=a2b2-a2b2co3Z(ab)=a2b2sin2N(a,A)yᦑ(ax2Î=a2b2(ab)2o3.()"axb=cxd,axc=஻xdj!ija-d²cᐳ5஺()(a-d)xS-c)=axb-axc-dx5+dxc=axZ>-cxd-axc+Z>xd=O,

13ᦑa—dcᐳ5஺4.()3-b)x(a+b)=23x/>),¹6)ᐸ;<,=஺()3-Z>)x(a+Z>)=axa+axZ>->xa-Z>xb=0+axZ>+ax)-0=2(«xZ>).ag?@ḄABC@DḄ*G5᪀ᡂḄABC@DḄ☢Ë8!a,b?@ḄABC@DḄ☢ËḄ2Ó஺5.ᙠGᙶ᪗¶”=(2,3,-1),6=(1,-2,3),a,b/ᚖy᝞Iᩩ¯¿Ḅᔣ.c(1)cᓫÖᔣ.%(2)cd=10,ᐸd=(2,l-7).ᔣ.ca,b/ᚖᡠc=Aax6,leiC2axb=23-1=(7,-7,-7),\axb\=7y[3.1-23ᓽ×x*l,|4|=Ø=Ùᦑ(1)cᓫÖᔣ.ᡠ|c|=l,C=±(1,—1,—1)஺#(2)ᵫtZ=(2,l-7),cd=10,2(14-7+49)=10,2=—,!"286.ᵨᔣ.():(1)uGDḄLÚÛᳮ⁐bsinAsin3sinC(2)uGD☢ËḄÝÞ(Heron)à99=á8⁐AuGDḄ☢Ëᐸ஺জcuGDu@Ḅã஺()(1)GA,",C*ä@⊤hḄᔣ.஺8c,ᵫᔣ.᜜ËḄåḄ;<,=⍝—|ax/>|=—|ftxc|=—|cxa|,!"TsinC=|fe||c|sinA=|c||a|sinB»222abᦑsinAsinj?sinC(2)A2=~\axbf=-(a2b2-(ab)2)=-(a2b2-aVcos2Z(a,Z>))444=~1(a,2b,2-a2b2(^a—+^b~1,-c—,)2)=~1(a2,b,21(,a2+b,2-c2,),2)4lab44=^(4a2b2-(a2+b2-c2)2)=^(2ab-^-a2+b2-c2)(2ab-a2-b2+c2)=C((a+b)2-c2)(c2-(a—6)2)=—(஻+b+c)(a+b—c)(c+a-b)(c-a+b)1616

14=p(p-a)(p-b)(p-c)o7.()Jacobiឤ89ax(஻xc)+2x(cxa)+cx(ax/>)=0஺()ᵫèé᜜Ëà9ax(bxc)-\-bx(cxa)+cx(axb)=(ac)b—(ab)c+(ba)c—(bc)a+(cb)a-(ca)b=0o8.aw0,0=x&êaxx=bḄxPḄëì஺ᵫ᜜ËḄÛ=í᜜ËåḄ;<,=xḄëìᙠ2ᚖḄA☢Tyîx஺AB!aḄ5Ḅ|}—Ḅ5lyïa,x,6ðñᢝió¶஺R⚪1.51.()(ax))c=Sxc)a=(cxa)஺()᝞a,஺,cᐳ☢ôiJ(axZ>)c=Sxc)a=(cxa)2=0஺᝞3ᐳ☢ᑣ|(஻x2)c\=\(bxc)a|=|(cxa)b\,{஺ùc},{ûc,a},{c,a,5}üᔠ~Ḅióᡈfóÿ|(axb)c(bxc)a,(exa)ᨵḄ^(axb)c=(bxc)a=(cxa)b9o2.a,b,cᐳ☢axxc,cxaᐳ☢஺m[(axb)x(bxc)](cxa)={[(axb)c]f)-[(axb)b]c}(exa)={[(axb)cp}(cxa)=[(ax஻)c][b(cx஻)]=[(ax()cf,ᡠ+(ax஻)c=0<=>[(axfe)x(Z>xc)](cxa)=0oᦑa,,cᐳ☢ax,஻xc,cxaᐳ☢஺3.ᙠ3456ᙶ᪗9:;<=☢>Ḅ⚔@A4(1,2,0),E(;1,3,4),C(-l,-2-3),D(0-1,3)KLḄ>M஺NA-214(AB,AC,AD)=-2-4-3=59,-1-33ᡠ+=☢>ABCDḄ>MV=1\(AB,AC,AD)\=y.ABCl)4.LagrangeឤST(axb)(cxd)=:(axb)(cxd)=a[bx(cxd)]=a[(bd)c-(bc)d]=(ac)(bd)—(ad)(bc)=bcbd5.(a+8஻+c,c+Q)=2(a,8c)஺A(a,b,d+e)=(ax)(d+e)=(axb)d+(axft)e=Z)+(a,b,e),ᡠ+(a+0,)+c,c+a)=(a+),)+c,c)+(a+஻,5+c,a)=(a+[\c)+(a+஻,c,c)+(a,஻+c,a)+S,)+c,a)

15=(a+[[c)+([)+c,a)=(஺,^,c)+(Ab,c)+S,5,a)+(Ac,a)=2(஺`c)஺6.(஺`cxd)+S,c,axd)+(c,a,)xd)=0஺bc=[(axb)xc]d+[(6xc)xa]d+[(cxa)xb]d={[(ac)b-(bc)a]+[(ba)c-(ca)b]+[(cb)a—(ab)c]}d=0d=0=3c஺7.efg=<ᔣia,஻,c,dᨵS,c,d)a+(c,a,d)A+(஻,(,d)c+S,a,c)d=0஺A(bcd)a+(bac)d=(b,c,d)a+(c,b,a)d=[(஻xc)d]a+[(cxb)a)]d9999=[((xc)d]a-[(bxc]a)]d=(bxc)x(axd),ᳮ(c,a,d)b+(a,b,d)c=(a,d,c)b+(d,a,b)c=(a,d,c)b—(a,d,b)c=(axd)x(bxc)ᡠ+S,c,d)a+(c,a,d)஻+(a,஻,d)c+((,a,c)d=Sxc)x(axd)+(Qxd)x(஻xc)=0஺8."a2bᐳlᑣ஺n(஺n஻)o஻n(஺*஻)ᐳl஺A஺oqᐳlᡠ+ax஻r0.ᵫtu*3v))]*3n(஻*)]={[0*(gn^)]3*஺)}x;{[஻*(஻v^)]b}(axb)=-{[ax(axb)]஻}(ax8)={[(ax஻)xa]b}(axb)=[(axb)(axb)](axb)=(axZ>)2(ax))w0,஻x(ax))ozx(ax஻)ᐳl஺9.{|a,஻}~ᦪᔣi஺[cḄᔠM3,8,c)=W᝞ᔣira-a/b=//c=0,Kᔣir஺Nᵫᩩᑮr(᜛a-aA)=0,rc=0,r=4(£a-a8)xc,ᙠcᑖoaᑁMᑣᨵa=ra-Xa[(pa-ab)xc]=-a2(a,fe,c)=-aapX&10.4,62,63ᐳ☢f;ᔣi஺+⊤ᡂa=-----3,஺2,஺3஺1+஺,஺2+3,4,43஺12஺3Aᐳ☢ᡠ+f;ᔣi஺+⊤ᡂa=XC]+7஺2+20஺cᑖoᔣi62X63,63xe¢eiX4ᑁMᑮ

16(«,e,e)=x(e,,e,e),(a,e,e,)=j(e,e,e),(a,e,,e)=z(ee,e)232331232p2Ja=~((a,e2,e,)C]+(4,63,e1)e2+(a,ei,e2)3)°(e,e,e)t2311.a,Z>,cᐳ☢ᔣirra=a,r/>=£,rc=7,¤¥ᨵr=——-——(abxc+ficxa+yaxb)஺(a,b,c)Aa,),cᐳ☢ᡠ+ax),Z>xc,cxaᐳ☢¦r=x(Z>xc)+j(cxa)+z(axZ>),cᑖoa,A,cᑁMᑣᨵa=ar=xa(bxc),j3=br=yb(cxa),/=cr=zc(axb),§~r=——-——(abxc+J3cxa+/axb)■,(a,b,c)¨©ª5lo«☢¬⚪2.11.K®¯@4(2,3,4)°3(5,2,-1)Ḅ5l^±஺x-2j-3z-4N5lḄ^ᔣᔣiA®=3ᡠ+5lḄ^±A3=-12.ᙠ²³Ḅ´µᙶ᪗9:K¶ᑡ«☢Ḅ¸®^±°¹ᦪ^±஺প¯@;1,2,0,-2,-1,4,3,1,-52¯@3,1—2°z»;3¯@2,0,—1°;½3,4,«¾§y»;4¯@-1,-5,4,«¾§«☢3x-2y+5=0஺NI«☢Ḅ^ÀᔣiAᓃ=;1,;34,ᓃ=4¢1,—5ᡠ+«☢Ḅ¹ᦪ^±x=-l-2+4/z,•j=2-32-//,z=44-5஻.«☢Ḅ¸®^±A

17x+1y-2Z-1-34=0,ᓽ19x+Uy+13z-3=0.4-1-52«☢Ḅ^ÀᔣiAᓃ=3,1,—2,%=0,0Jᡠ+«☢Ḅ¹ᦪ^±x=3+32,■=1+4,A¯z»ᡠ+`⌱ůḄ@A0,0,0,¤¥¹ᦪ^±`+[z=-2-2A+x=3/1,ᑏAÇy=Èz=-22+«☢Ḅ¸®^±Axyz31;2=0,ᓽx—3y=0.0013«☢Ḅ^ÀᔣiAᓃ=;A3,5,ᓃ=0,1,0ᡠ+«☢Ḅ¹ᦪ^±x=2—3A,■j=32+//,[z=-l+52.«☢Ḅ¸®^±Ax-2yz+1-335=0,ᓽ5x+3z-7=0.0104«☢Ḅ^Àᔣi«¾§«☢3x—2y+5=0,^ÀᔣiX,y,Z3X-2F=0,+⌱Aᓃ=2,3,0,%=0,0,1஺ᡠ+«☢Ḅ¹ᦪ^±x=—1+2A,•y=—5+34,z=4+4.«☢Ḅ¸®^±Ax+1y+5z-4230=0,ᓽ3x—2y—7=0.001

183.ᙠ56ᙶ᪗9:K®¯@(1,0,-2)Éo«☢u121+7-2-2=0°02*7-2-3=0ᙳᚖ5Ḅ«☢^±஺N«☢u”ÍḄÎᔣiᑖ~Ï=(2,1,-1),%=(1,;1,;1)ᡠK«☢ou”u2ᙳᚖ5ᡠ+LḄÎᔣi஻o஻ᙳᚖ5n=n,xn=(2,1,-1)x(1,-1,-1)=(-2,1,-3),2«☢Ḅ^±A;2(x—1)+y—3(z+2)=0,ᓽ2x-y+3z+6=0.4.ᙠ56ᙶ᪗9:Ků@஻](3,-1,4),“2(1,0,-3),ᚖ5§«☢2x+5y+z+l=0Ḅ«☢^±஺N«☢ḄÎᔣiA஻ᑣLoÕÖᚖ5Lvo«☢2x+5y+z+l=0ḄÎᔣi(2,5,1),ᦑ஻=(;2,1,-7)ஹ(2,5,1)=12(3,-1,;1).ᡠ+ᡠK«☢Ḅ^±A3(*_3)—(y+1)—(z-4)=0,ᓽ3%—y—z—6=0.5.ᙠ56ᙶ᪗9:«☢IIḄ^±AAx+3y+Cz+O=0,ᐸ:A6C0HO஺«☢oÜᙶ᪗»ᑖݧ,KÜ6ÞḄ☢M°=☢>0MlM2M3Ḅ>M஺Nᵫ§A5CDH0,ᡠ+«☢ḄÜ<àáᑖA;2,-2,-2஺=☢>ABC2M3Ḅ>MAV=~1236ABC6\ABC\Ü6Þäå2,M3Ḅ☢MS=æ|Må2XM]M3],M.MxAf.Af,=;,——,0x;,0—=D2---,12213ABACBCCAABD2ylA2+B2+C2ᡠ+S=2ABC

196.«☢n:Ax+5y+Cz+஺=0oçè@.(é,+,4)°M(x,y,z)Ḅl2222êݧ@Mæk=bìík_AX|+By+Cz+DxtAX+By+Cz+D222A,ᡠ+ᵫ³îᑖ@Ḅᙶ᪗ïTᑮ@ðḄᙶ᪗X=X'+kX\yJ+”Z=ó`■ôLõöᐭ«☢^±:1+k,1+k1+k4kx?+B%+Q?.+cø++2.+0=0᦮ᳮᓽ\+ki+k1+kk_AXj+By+Czj+DxAX+By+Cz+D222¬⚪2.21.Ků@(-2,1,3),É®¯«☢2%-7t+4%-3=0o3*-57+4஽+1=•ḄÝlḄ«☢^±஺NůÝlḄ«☢ü^±A4(2x-7y+4z-3)+4(3x—5y+4z+l)=Ḅᐸ:44ᐰA஺ᡠK«☢ů@(;2,1,3),ôLöᐭþTᑮ4—64=0,+ÿ4=6,4=1,☢Ḅ15x-47y+28z-7=0.2.ᑨᑡᔜ☢Ḅᐵ஺(1)x-2y+z-2=(^3x+y-2z-l=04(2)3x+9y-6z+2=02x+6y-4z+§=0(3)x+2y-z-1=0—l-_y——+2=0o22(l)☢Ḅ!ᔣ#ᑖ%&(1,'2,1),(3/,'2),()*ᐳ,-ᡠ/0☢1஺(2)0☢Ḅ2ᦪ45Ḅᐵ26=2=7=§,ᡠ/0☢:ᔠ஺26-443(3)<=>☢Ḅᓄx+2y—z+4=0,ᡠ/0☢Ḅ2ᦪ45Ḅᐵ2

20121-1ᓝ'=—=-H---Aᡠ/0☢B஺12143.CᑡD,ḄEFᓄ᪗H஺3x-j+2=0,y-1=0,(1)4(2)V4j+3z+1=0;z+2=0.13x=j-2,xj-2z+3(1)Iᑏᡂᡠ/᪗H[4(j-2)=-3(z+3),(2)᪗HL=ᓃ1="21004.NFOPN0(l,4,-2)Q0☢II]:6x+2y+2z+3=0EI,:3x-5j-2z-l=02ᙳSḄD,஺TD,Ḅᔣᔣ#v=(x,y,z)UV0☢ᙳS-ᡠ/6X+2Y+2Z=0,WᑮXy:Z=1:3:(-6),3X-5V-2Z=0Y&D,Ḅx-1_y-4_z+2=—•13-65.ᑨᑡᔜD,Ḅ஺.,.x+1j-1z-2xy-6z+5(1)------=-------=-------.----=-------=-------331-123X4-j+Z=0,]X+Z4-1=O,(2)4j+z+l=0,[x+y+l=0.r+1v—17—2(1)D,Z:'=\'=3']OPᔣᔣ#&ᓃ=(3,3,1),D,^=_?==]OPM(0,6,-5),ᔣᔣ#&a=(-1,2,3)஺2—12315-7bᔠc(de,ᓃ,ᓃ)=331=-106஺0,ᡠ/0D,f☢஺-123

21fx+y+z=O,[x+z+l=஺,Iᑖ%ᓄx-lJ+1z(2)D,.j+z+l=O,[x+j+l=O.*==.]OḄPᑖ%&M/1,-1,0),M(-1,0,0).ᔣᔣ#ᑖ%&2010ᓃ=(0,1,-1)/2=(-1,1,1)bᔠc(ᯠd#”%)=01-1=100,Qᓃ%=°ᡠ-111/0D,f☢QkᚖD01=7+26.ND,☢x-2j-7=0Ḅ1P஺j=l-3zTCD,mn☢Wᑮz+2-2(l-3z)-7=0,ᡠ/z=l-ᦑ1P(3,-2,1)஺3x—4y+5z—1=07.NFOD,+_QD,4*=29=32SḄ☢஺3z40TFOD,4Ḅ☢It2(3x-4j+5z-l)-M)U(2x+2j-3z-4)=0,ᵫY☢D,4S-ᡠ/6(34+2஻)+3(-44+2஻)+2(54-3஻)=0,ᓽ44+3w=0,ᦑ☢x-20j+27z-14=0o8.ᙠDyᙶ᪗2{-ND,|:L4=2=ஹ3ᙠ☢nx+2y—6=0ZḄᚖDᢗD,Ḅ஺TᚖDᢗD,ᙠOD,/QᚖDY☢nx+2y—6=0Ḅ☢{-☢௃ḄX-lJ+1Z-32-14=—8x+4y+5z-3=0,120ᡠ/ᚖDᢗD,&+2y-6=0,8x-4y-5z+3=0.

229.ᙠᙶ᪗2{-NOD,:12"',-27+1=°Qᙠ97ZᨵḄx+y+4z-2=0Ḅ☢஺TFOD,-Ḅ☢It4(2x—y—2z+l)+஻(x+y+4z—2)=0,ᵫY☢ᙠyzZᨵḄ-ᡠ/';1+஻=-21+44ᓽ;1=3//,ᦑ☢7x-2j-2z+l=0.10.ᙠA45C{-tP,?,Rᑖ%&D,ZḄP-Q⊟=4d-BQ=nQC,CR=vRA1,L,AQ,BR,CPᐳPḄᐙ⌕ᩩ&v=1஺T᪗{4;/},ᑣPA,B,C,P,Q,RḄᙶ᪗ᑖ%&4(0,0),5(1,0),C(0,l),P(-—,0),0(-).D,AQ,BR,CPḄ1+21+M1+41+vᑖ%¡=2—=^-,஺-'L,AQ,BR,CPᐳPḄᐙ⌕ᩩ&1n1+v-12-(1+2)Ḅ1PᙠD,CPZ஺Ḅ1P(——1——,'4'),C¢PḄᙶl+஻+஻y1+//+//V᪗mnD,CPḄ{ᓄ£Wᑮ=1஺11.ᵨᙶ᪗!᜿¦§ᳮT©LyªḄL«¬ᑖᒘᡂ2:஻/:2,஻Tv,ᐸ{ᙳ±²ᦪ-ᑣLyªḄ⚔P«ᑖPḄ´,1Y'P஺TᵫY2Zµ=1,ᵫZ⚪Ḅ·¸V⍝LyªḄ⚔P«ᑖPḄ´,1Y'P஺஻4VA.x+B.1y+C1z+I>|=0,12.᝞»D,¼½ττD,[AX+By+Cz+£>2=஺222A.x+BQ+C.z+£>,=0,33%33-1Y..P-¾¿AX+B4y+Cz+Z>=04444&5'3=0o4(A4)a

23TᵫY0D,1Y'P-ᡠ/ÀAx+By+Cz+A=0,ixiAx+By+Cz+D=0,22224nᨵX஺4஺*஺Â-AX+B3y+Cz+O3=0,33AX+B4y+Cz+A=0,44AjX+By+Cz+=0,{xAx4-By+C,z+£>w=0,7ᑣÃÀ■/JÅnnᨵÆ/-Ç⊟஺/Â-ᵫÃ,ឋÀᨵAX+By+Cz+O3W=0,333AX+By+Cz+DW=0,44444B\G44GD2ḄᩩWᑮ=0OB3C3D3B4C4£>4T—1V+1713.ᙠDyᙶ᪗2{-ɧPMj(l,0,3)Ê2(0,2,5)D,/T——=--=-213tᔜMM2ᙠ-ZḄᚖË-N/ÌḄᙶ᪗஺Tᔣ#=(-1,2,2)ᙠD,/Ḅᔣᔣ#V=(2,1,3)ḄᔣZḄᑖMMV6{2#-ᦑMi'M=H=dOPM/1,0,3)ÍD,/ᚖDḄ☢,(Ḅ2(x—l)+y+3(z—3)=0,OPÊ2(°2,5)ÍD,/ᚖDḄ☢2,(Ḅ2x+y-2+3(z-5)=0,CD,ceḄÎᦪÏ=1+2/"=—1+/,2=3/ᑖ%mn1,2{-W4=Ð"2=/ᡠ/W,17215ஹ._.23124ஹMஹ9௄;௄

24D,/ḄLÝ=2=L-ᓽ,m—km1J=᝖,àáA:WᑮD,I᪀ᡂḄÕ☢y=xzxz,-+—1---———115.TᒹåD,æççc,QSYD,6TacḄ☢x=0j=0XVZ1111''1'L+1=0஺©)&4,44éḄê-F==+f+=abc12d1a2b2c2)íiTᒹåD,|T4஻CḄ☢It1%+஻(1+£-1)=0,(Ḅ!ᔣ#Öbex=0⁐-_(3ឌ)-(ðD,4Hac'S-D,Ḅᔣᔣ#&ᓃ=3,0,c),ᡠ/bcy=0(a,0,c)(4,µ,µ)=0,Wᑮ஺4+஻=0,Y&☢='Z'L+1=0஺bcabcD,4Ḅᔣᔣ#&ᓃ=((),b,—c),]OP×(0,0,c)஺D,4]OP஺(0,0,—஺)-ᡠ/0D,Ḅê2d=002c(PQ,v,v)=0b-c=-2abc>vxv=(0,b,-c)x(a,0,c)=(bc,-ac,-ab)t2t2a0c1_(be)2+3c>+(ab)2ᦑV+",4J7-4(abc)2d2a2b2c2ò⚪2.31.ᙠDyᙶ᪗2-NᑡD,஺(1)OP/o(—1,2,9)QᚖDY☢3x+2y-z—5=0(2)OP஻஺(2,4,—1)QLᙶ᪗ᜳyô஺(1)D,Ḅᔣᔣ#&☢Ḅ!ᔣ#v=(3,2,—1),ᡠ/D,Ḅ

25x+1y-2Z-93~~2(2)tD,Ḅᔣᔣ#&v=(x,y,z),ᵫYD,Lᙶ᪗Ḅᜳyô-ᡠ/|v(l,O,O)|=|v(O,l,O)|=|v(0,0,1)|,Y&ᑄ=|y|=|Z஺D,ᨵ4ᩩ,x-2_y—4_z+lx-2_y-4_z+1———=—1111-11x-2_j-4_z+1x-2_j-4_z+1——"=-o11-11-1-12.ᙠDyᙶ᪗2{-N☢-z+c=0xOy☢Ḅᜳy஺T☢ax+ö'z+c=0Ḅ!ᔣ#஻=(4÷'1),xOy☢Ḅ!ᔣ#=(0,0,1)-ᡠ/ᜳyḄøùcos®=-/1,ᜳy+b2+1C1T1Q=arccos/,ᡈr'arccos/.y/a2+b2+1y/a2+b2+13.Nᑮ0>ɧ☢Ḅêᡂ§5ḄPḄûü஺TtPM(x,y,z)ᑮ0☢Ḅê454>0஺᝞»0☢S-ᑣ⌱Dyᙶ᪗2þWᐸ{'>☢xOy☢-ÿ
☢Ḅz—d=0,d>0,z|=|z-d|=1z=4஺Axl(l±A)z=d.2᝞☢ᑣ⌱☢Ḅᑖ☢ᙶ᪗☢xQyxOzᑣ☢Ḅy+cz=0,y—cz=0,c>0,k\y+cz\=|y-!,ᓽ(l+k)y—(l±k)cz=0.4.%&'()*+,ᩩ.ᵨ+3+10)Ḅ34*5ᙠ73⚔3ᙠᙶ᪗9:;⚔3<*5=>aḄ?☢@ḄᑁB஺%&'ᩩ.|x|+3+|z|0)CD?
ECF'±x±y±z0),GH3I☢±x±yJz=a(a>0)ᩭLMᙠNOᓽᒹQ73ḄR•O஺ᦑUV4ᵫ?
☢JxJyJz=஺3>0)᪀ᡂ⚔3ᙠᙶ᪗9:;⚔3<*5=>aḄ?☢@Ḅᑁ

26B஺5.ᙠ[\ᙶ᪗]*M(X1,y”Zi)஻2(X2a20)MEᙠ☢II:Ax+By+Cz+D=0:;M|0M2஺%&'M1dḄ☢஺'3M(x,y,z)ᑮ☢Ax+<+Cz+O=0Ḅ=>d,Ud\Ax+By+Cz+D\-yjA2+B2+C2ugᡠ~☢ḄAx+By+Cz+D±dy]A2+B2+C2=0.7.~3M.(3,-1,2)ᑮpq-x-y+z-1=0,Ḅ=>஺[x+y—z+l=0'pqḄ᪗F

27±==ᡠ|pq3M(O,—1,O)ᔣᔣv=(O,l,l)ᑣdMMxv=(-2,3,3)3M/3,-1,2)ᑮpqḄ=>d=(H8.~ᑡᔜIpq)Ḅ=>஺X4-1_J-1_Z+5x_y—6_z+5-1=3-9~^6~xy+2z-1x-1j-3z+1x+j—z+l=O,[x—2j+3z—6=0,(3)x+y=0,12x—y+3z—6=0.'(1)pqᑖ3Mi(-L,l,-5),஻2(°6,-5)ᔣᔣᑖᓃ=(1,3,2),ᓃ=(3,—9,6),upqiUVḄ=>pqḄ3ᑮ♦pqḄ=>,ᡠ|=(1°-2,8),UVḄ=>MJMxV,2=>=26V14(2)pqᑖ3(0,-2,1),A/(l,3,-l),ᔣᔣᑖ2ᓃ=(2,-2,-1),%=(4,2,-1),M,M=(1,5,-2),v,xv=(4,-2,12),22(MM,v,v)=MM(V,XV)=-30,ᡠ|UV☢UVḄ=>i2l2l22,|(]2%,ᓃ)|3015==g(3)pqḄ᪗Fᑏ'=2•==,=:=2,pqᑖ3M](0,0,1),M(0,0,-2)2ᔣᔣᑖᓃ=(1,-1,0),%=(1,—1,1)ᓃ஽Eig=(0,0,—3),ᑭᓃ=(1,1,,0),(g,ᓃ,ᓃ)=gM(%¡ᓃ)=0,ᡠ|UVUVḄ=>0஺

289.~ᑡᔜIpqḄ¢ᚖqḄ஺(1ஹ)1yz:xyz“1=¦=<=ᓃ=——¨-3321-2sஹfx+j-l=o,fx-z+l=o,(3)<©z=012y+z—2=0.(1)pqḄᔣᔣᓃ=(1,3,3),%=(2ª,2),ᡠ|¢ᚖqḄᔣᔣv=Vjxv=(3,8,7)o2y=«;<ᔣ¬=(3,8,7)iḄ☢:☢ᔣ¢ᚖqᙠpqx-l=%=(3,8,7)x(1,-3,3)=(45,-2,-17),ᡠ|®☢45(x-l)-2j-17z=0«¢ᚖq¯ᙠpq¦=£=¦¨;<ᔣv=(3,8,7)iḄ☢:☢ᔣ21-2n=(3,8,7)x(2,1,-2)=(-23,20,-13).ᡠ|®☢23x—20y+13z=0u2¢ᚖqḄ45x—2y—Viz-45=0,23*—20y+13z=0.(2)pqḄ᪗Fx-1yzx-1yz-2-f-~—,1-102-12ᡠ|¢ᚖqḄᔣᔣv=(1,-1,0)x(2,-1,2)=(-2,-2,1)஺¢ᚖqᙠpq—=©=";<ᔣv=(-2,-2,1)iḄ☢:☢ᔣn,=(1,-1,0)x(-2,-2,1)=(-1,-1,-4),ᡠ|®☢x+y+4z-l=0஺X—1V7—2¢ᚖq¯ᙠpq:=:=^—,;<ᔣ³=(2,-2,1)iḄ☢:☢2-12ᔣ%=(2,—l,2)x(—2,—2,1)=(3,-6,-6),ᡠ|®☢(x-l)-2j-2(z-2)=0,u¢ᚖqḄx+j+4z-l=0,x—2y—2z+3=0.

2910.~ᑡᔜIpqḄᜳ஺x-1y-3z+4x-1yz-1(1)-----=-----=-----,-----=—=-----;-112-24-3[x+j+z—1=0,[3x+j+l=0,(2)>x+j+2z+1=0,[j+3z+2=0.(1)pqḄᔣᔣᓃ=(1,1,2),ᓃ=(2,4,—3),ᡠ|ᜳ+,COS0==0,uᜳº஺(2)pqḄᔣᔣᓃ=(1,1,()),%=(1,—3,1)
ᡠ|ᜳ+,AV,V\2V2222₹᪆F'J22J22uᜳ0=arccos----•ᡈ6=;r-arccos------.111111.~ᑡpq<☢Ḅᜳ஺r—1v7+I(1)/'-y==nX-2j+4z-l=0x-y—z+2=0,(2)II:2x—z+1=0.2x—3y+3=0'(1)pqḄᔣᔣy=(2,1,—1),☢Ḅᔣ஻=(1,2,4),ᑣ42V14m.....•2714v஻=4,ᡠ|ᜳ+,sin6=ª-----uᜳ0=arcsm-------V6V2I2121(2)pq/ḄᔣᔣÃ=(3,—2,—1),☢Ḅᔣ஻=(2,0,—1),ᑣ5V70ᓝ&"•V70v஻=—5,ᡠ|ᜳ+,sin஺=—=I—l=----uᜳ0=arcsm------.71475141412.Årᩩ☢pq4<4%&'ÇÈ4:É3ᑭ<:É3ḄqÊḄ*3ËÌ¢ᚖqÊḄᚖpᑖ☢஺%&'|¢ᚖqz9¢ᚖqÊḄ*3<¢ᚖqᚖpḄ☢xOy☢☢pqᙠxOy☢:ḄᢗÑpqḄᑖqx9y9ÒÓ()pᙶ᪗]஺ᑣ☢pqḄ

30-=y-=t<=:=H,ᐸ*2apqḄ=>k>0஺1k01-k0ÕᙠÖpq:ᑖÉ×39h,a),(s,-As,—a),ᑣUVḄ*3(x,y,z)+,x=—,j=fe(r-y),z=O,G¢ᚖqÊḄᚖpᑖ☢ḄØᦪᡠ|*3Ë22Ì¢ᚖqÊḄᚖpᑖ☢஺13.ᙠpᙶ᪗]*☢n|Cᡠ||2x-y2z-3|=|3x+2-6z-l|,ᵫ®¦☢ᑁᨵ3p(i,2,—3),;21-2+2(—3)—3=—9<0,31+22—6(-3)-1=2¥0,ᡠ|Ý(1,2,-3)ᙠn1ḄNOᙠn2ḄÞOuᑖ☢:Ḅ3ᙠn|ḄNOᙠnÚḄÞOᡈᙠn1ḄÞOᙠn2ḄNOᡠ|ᑖ☢:Ḅ3+,7(2x-y+2z-3)=-3(3x+2y—6Z-1)᦮ᳮᑮ23x-y-4z-24=0.14.%&'☢pq"4Ḅ¢ᚖqÊḄáâã4ä)Ḅ=>஺%&'|¢ᚖqz9¢ᚖqÊḄ*3<¢ᚖqᚖpḄ☢xOy☢☢pqᙠxOy☢:ḄᢗÑpqḄᑖqx9y9ÒÓ()pᙶ᪗]஺ᑣ☢pqḄä'J=:=¦åᓽ¢ᚖqÊ11k021-k0Ḅáâ>0஺ÕᙠÖpq:ᑖÉ×3P(t,kt,a),Q(s,-ks,-a),3=>▀³yl(t-s)2+k2(t+s)2+(2a)2>2a,ᓽ¢ᚖqÊḄáâᨬèḄu☢pq஺4Ḅ¢ᚖqÊḄáâã4஺)Ḅ=>஺

31éêëìí☢î⚪3.11.%&'᝞/+/+஺2—d>0,Rñᵫx2+y2+z2+2ax+2by+2cz+d=0òóḄí☢ᳫ☢~óUḄᳫ5ᙶ᪗õö஺%&'÷ø(x+«)2+(j+Z>)2+(z+c)2=a2+b2+c2-d,ᵫ7+02-^>஺ᑮ⊤þᳫ5(-a,-b,-c),õöyja2+b2+c2-dḄᳫ☢஺2.~3(3,0,0),(0,2,0),(0,0,1)ḄᙊḄ
஺Ḅᙊᵫ(3,0,0),(0,2,0),(0,0,1)Ḅᳫ☢☢Ḅ⊤Ḅᳫ☢
X?+J?+/+ax+5y+cz+d=0,ᑮ9+3a+d—0,<4+2஻+d=0,l+c+d=09+஻4+dᳫ☢
/+y2+z2%—_j_y_(l+d)z+d=0,ᐸd*+஺Ḅ☢
,-+2+Z=1,ᡠ0ᡠ1ᙊḄ
0326(x2+J2+Z2)-2(9+J)X-3(4+J)J-6(1+J)Z+6J=0,<2x+3y+6z—6=0ᐸd*+஺3.89:tX=-----z----l+t2+t4t2■y=1+.+=fe(-oo,+a>)t3Z=l+t2+t4ᙠᳫ☢EFGᳫ☢
஺89H:IJ

3213x*2*+j2+z2=(-~~)2+(-~r—r)2+(-^~)2?r1+/+஻1+f2+rl+r+t=(;—5—?)2(1+஻+஻)=-i—=yl+t2+rl+t2+rᓽx2+(y-JL)2+z2=L,ᡠ0:ᙠᳫ☢E஺244.〉w⌱yᙶ᪗\1]ᑡ{|Ḅ
(1)ᑮ}~ᦪḄḄ{|(2)ᑮ}~ᦪḄḄ{|(3)ᑮ~☢~ḄḄ{|஺(1)⌱cdᙶ᪗\~ᙶ᪗(0,0,஺),(0,0,-஺)஺~ᦪA0஺ᡠ0(x,y,z)IJ/+/+(z-q)2=/(J+/+(z+“)2),ᓄUᨵ(l-k2)x2+(l-k2)y2+(l-k2)z2-2a(l+k2)z+(l-k2)a2=0,w4=1{|☢z=0஺ii-2+w0W1{|ᳫ☢“2+y2+2'_^z+"2=0஺1-k2(2)⌱cdᙶ᪗\~ᙶ᪗(0,0,a),(0,0,-”)஺ᦪ0஺ᡠ0(X,y,Z)IJ+y2+(z—a)2++y2+(z+a)2=k,ᓄUᨵ4k2x?+4k2y2+(4k2-16a2)z2+4k2a2-k4=0.(3)⌱cdᙶ᪗\~ᙶ᪗(0,0,a),~☢z=-a.ᡠ0(x,y,z)IJy]x2+y2+(z-a)2=|z+«|,ᓄUᨵx2+j2=4az.5.:☢SᙠY☢ᙶ᪗\]Ḅ
v=R2cos2஻1SḄcdᙶ᪗
஺eY☢ᙶ᪗fgdᙶ᪗Ḅᐵ\x=Rcosu,y=Rsin஻,z=vkᐭ
ᑮ22x-y=z.6.:☢SḄcdᙶ᪗
x2+y2-z2=25,m1ᐸᳫ☢ᙶ᪗
஺eᳫ☢ᙶ᪗fcdᙶ᪗Ḅᐵ\x=Rcos0cosg),y=7?cossin(p,z=Rsin®kᐭ
ᑮx2+j2-z2=R2cos20-R2sin26=25,ᓽR2cos20=25.

33⚪3.21.11,x=E=ḄᙊY☢
஺23ᙊY☢EḄ(x,y,z)ᑮx==ZḄ,ᦪ1ᡠ0|(x,yz)x(l,2,3)|ᓽᨵ+3%)2¢==12+(2x14V1+4+92.£¤fᙊY☢Ḅᩩ¦x=y=z,x+l=y=z-l,x-l=y+l=z,1§ᙊY☢Ḅ
஺ᐜ1EḄ(x,y,z)ᑮ¦Ḅ©ᡠ0|(x,j,z)x(1,1,1)|=|(x+l,j,z-1)x(1,l,l)|=|(x-l,j+l,z)x(l,l,l)|,ᓄU᦮ᳮḄ
x=y+l=z-loᙊY☢EḄᑮḄEḄ(0,—1,1)ᑮ¦x=y=zḄᡠ0|(x,j+l,z-l)x(l,l,l)|=|(0,-l,1)x(1,1,1)|,ᓽ(y—z+2¢+(x—z+1¢+(x—y—I)2=6,¬ᑮᙊY☢
x2+y2+z2—xy—xz-yz+3y—3z=0.3.1¦
ᔣ(2,—3,4),¯|+==%ḄY☢
஺Z=1Y☢EḄ~ᙠ°¯E(±0²/0)Ḅ¦Eᡠ0X+³=9,஺=1,'x=x+2t,0y=y-3t,0z=z()+4r´µ¶·⊟஺"ᑮY☢
16x2+16y2+132+24yz-16xz+16x-24y-26z-131=0.Z4.£¤ᙊY☢Ḅ2x=l-y=-z+l(1,2,1)ᙠGᙊY☢E1GᙊY☢

34Ḅ
஺ᙊY☢EḄ(x,y,z)f(1,2,1)ᑮḄ©ᡠ0|(x,j-l,z-l)x(-l,2,2)|=|(l,-3,0)x(-1,2,2)|=41,¬᦮ᳮ8x2+5y2+5z2+4xy-8yz+4xz—8x—2j—2z—39=0.5.1¯•72=i,ḄᙊY☢
஺z=0H¯,ºᙊᡠ0ᙊY☢Ḅ~ºᙊḄ»(0,0,0),¦
ᔣ¼½¾ᙶ᪗☢xOy,(/,,1)஺ᙠ¯Ey(2,0,0),(0,1,0),(¿,1,0),À2ÁᑮḄÂᙊY☢Ḅr,|(2,0,0)x(/,/n,l)|=|(0,l,0)x(Z,«,l)|=(V3,1,0)x(Z,/n,l),I4+4஻/=1+஻=L+3+(¿Ã,/)2,ᓄUᨵ42I'Äᯠ/஺0,ᡠ0஻=0"=-JJ.r=1஺HÆᙊY☢ᨵ}|(x,y,z)x(-=4,ᓽ(x-Ç¢+4/=4.rr6.10Zᙶ᪗È⚔⚔dᝅḄᙊ┵☢
஺Hᙊ┵☢0Zᙶ᪗È⚔⚔dÌᡠ0ᙊ┵☢Í6x2+j2—z2tan2—=0,BP3x2+3j2-z2=0.67.1⚔ᙠȯḄ┵☢
஺Z=h,(h0)┵☢EḄ(x,y,z)~ᙠ°¯EÎ(/Ï,7)Ḅ¦.Eᡠ0

35/(*0R)=°Zo=h,.X஺=tx,HGᑮ┵☢
/(—^)=0.ZZy°=Os/o=tN8.10È⚔ᒹÓᩩᙶ᪗Ḅᙊ┵☢
஺ᙊ┵☢ḄḄ
ᔣᔣÔ(/,᪷,஻)Ö᯿⚪+Ḅ
ᔣᔣÔfᙶ᪗Ḅᙶ᪗ᔣÔḄᜳdḄÙÚḄÛÜ©ᡠ0ᨵ|(1,0,0)(Z,m,w)|=|(0,l,0)(Z,m,n)|=|(0,0,l)ᓽ|Z|=|/n|=ÝḄ
ᔣᔣÔ(1,±1,±1)஺HGᙊ┵☢EḄ(x,y,z)IJ|(j,y,z)_1ᓄUy±yz±xz=0.ᓽᨵÞᙊ┵☢஺XVX2+/+Z2V3V3P.£=19.1⚔(0,1,0),¯â4'Ḅ┵☢
஺z=-5┵☢EḄ~ᙠ°¯EÎ(“஺²”஺)Ḅ¦ᓃᡠ0%0=-5,•x=tx,HGäIJ┵☢
20x2-5y2-z2+2yz+10y—2z-5=0.0y=l+/(j-l),0஺=z10.89¦
ᔣ(/,஻?,஻)fᳫ☢/+/+d=1᜜ᑗḄY☢
(lx+my+nz)2—(I2+m2+n2)(x2+j2+z2-1)=0089Ö᯿⚪+¤Y☢,1ḄᙊY☢=E=±.ᡠ0Y☢EḄImn(x,y,z)IJ|(xy,z)x(",ç=],ᵫéêᑮyll2n2+n21'+t(Z2+m2+n2)(x2+y2+z2)-(Zx+/nj4-nz)2=I2+m2+n2f

36ᦑY☢
(Zr+"Z)2+"2)(*2+y2+஽2-1)=Q஺11.xyᑖîï☢d஺ᦪ1Ḅ{|
Fð89À,••┵☢஺xyḄ☢
5j+C,z=0,AX+Cz=0.ÀÁḄ,22fB.j+C.z=0,111ᵫ}☢Ḅd,ᦪᡠ0AX+CZ=0.22cc|cose|=,l>jK=,
Ḅ\ᦪᢥGᐵ\´µᑮ{|
x2j2-cos20(y2+z2)(x2+z2)=0,
9Ä,4òóò
ᡠ0,┵☢஺12.890Af(x,j,z)⚔Ḅ┵☢
,ᐵ(x-x0),(y—ôõö7஺)Ḅó0000ò
஺89ᡃÁ¤⍝⚔ᙠÈḄ┵☢
,ᐵx,y,zḄóò
ᡠ0eᙶ᪗\ḄÈùᑮM(x,y,z)&úᙶ᪗\Ḅᙶ᪗ᵨ*',_/,/ᑣ0000x=x-XoV=y-y,,z'=z-Zoᦑ┵☢
,ᐵx',y',z'Ḅóò
ᓽᐵ(x-x),(y-y),(z-z)Ḅóò
00013.1]ᑡ:ᔣᔜᙶ᪗☢ᢗÿḄᢗ☢ᙠᔜᙶ᪗☢ḄᢗḄx2+y2=4a2,(x2+j2+z2=4,(x2+y2+z2=4a2,x2+2y2+z2=5a2;[x2+(y-3)2+z2=4;[x2+y2-2ax-0.(1)ᔣxQy☢ᢗḄᢗ☢/+_/=*2,ᙠxOy☢Ḅᢗx2+j2=4a2,z=0.ᙠx!ᑮᔣyOz☢ᢗḄᢗ☢y2+z2=a2,ᙠyOz☢Ḅᢗy+z=ax=0.ᙠj!ᑮᔣxOz☢ᢗḄᢗ☢x2-z2=-a2,ᙠxOz☢

37Ḅᢗ$=0.(2)ᙠᑖ'x,y,z!ᑮᔣyOz,xOz,xOy☢ᢗḄᢗ☢ᑖ'72y-3=0(|x|42,|z|2),x2+z2=-,2j-3=0(|x|<2,\z\<2).ᙠ☢Ḅᢗᑖ'7J2y-3=0X2+Z2=4J2J-3=0b=0,0"2)4ஹ(|#2).[y=0,i(3)ᙠᑖ'x,_y,z!ᑮᔣyOz,xOz,xOy☢ᢗḄᢗ☢ᑖ'Z4—4a2z2+4஺2y2=0,z2+2ax-4a2=0,x2+y2-2ax-0஺ᙠyOz,xOz,xOy☢Ḅᢗᑖ'Z4—4a2z2+4a2j2=0,z2+2ax—4a2=0,x2+y2-lax=0,<~<f))Ḅ:ᡠ@☢Ḅ9x=f(t)+ls,

38xo+Jo=17=᮱-"0R0S0ₔ!ᑮIJ☢ḄX2+J2=l,ᵫVWx2+y2=xl+ylz-z=0,oOWzWlḄXYᑖᡠ@IJ☢ZXYᑖx2+y2=l,0⊟0)(hiḄ7ᦪ9I஺)IJᩭḄ,X=/(%)9=g«o)Zo=h(t),0•+y2=xj+yj,Z_Zo=0ᡠ@☢Ḅ7ᦪlᑏ9x=ylf2(t)+g2(t)coe,•J=ylf2(t)+g2(t)Sina(0W”2n).z=h(t),4.opz=X^~r⊤tXuIJ☢;NḄ:JH஺X+y

39opḄvwlᦋᑏ9(/+y2)z=l,{|@JZ=l'ᡈJ*Z=l'9:x=0[j=0zH9IJHBl!ᑮ☢Ḅ஺C⚪3.41.Xuᳫ☢@]uᙶ᪗☢9h☢L=]u<(2,2,4),(0,0,6),(2,4,2),;ᐸ஺72+0=1,]u<Ḅᙶ᪗ᐭ!ᑮ5ᳫ☢Ḅ9r+a2b24416,/+”¥=1!஺2=9,=36,=36,4164r-V+—r+-r=la2b2c2ᡠ@ᳫ☢Ḅ9^++U936362.;@<9⚔<zH9hH=<(3,0,1),(3,2,2)Ḅᱥ☢Ḅ஺5ᱥ☢Ḅ9ᱏ+ᱏ=2z,u<Ḅᙶ᪗!ᑮab9949x2v2-=2,-+-=4,!a==,b=2,ᡠ@ᱥ☢Ḅ9^+2=4z.aab2943.;=ᩩᱥ1*-6=஺+=°'Ḅ^☢஺z=0[x=05^☢9Xax2+ay2+«z2+2axf2ayz+2ax±2ax+2ay+-ba=0n2133n2313i4u44ᵫV☢=ᩩᱥᡠ@x=0,z=0ᑖ'!ᑮᩩᱥax2+ay2+2axf2ax+2ay+4/^=0,n22l2i424z=0.a22y2+a33^2+2a23yz+2a24y+2az+a=0,3444x=0

40`¡Ḅᱥ¢£¤¥!ᑮᡠ@☢Ḅ9X+,஺24¦+2«13*%+2a24y=஺ᐸ஺“஺¨©ᐰ9°஺32K“24=0«.9xz=0KaAo«.lᓄ924X2Z2--X¯X2Axz-2y=0,ᐸ°9±²³ᦪ஺4.¡´X2y2x2—~~-+-5X-+—~~-=1(a>b>c>0),a-kb"—kc—k¶K·¸¹V஺2,b2,஺2Ḅᔜº»ᦪ¼«N⊤t½᪵Ḅ☢¿ᵫVa>b>c>0,ᡠ@K<஺2«a2-k>0,b2-k>0,c2-k>0,⊤tᳫ☢ÃK஻2>>஺2«a2-k>0,b2-k>0,c2-k<0,⊤tᓫÆÇ☢ÃK஺2>4>>2«a2-k>0,b2-k<0,c2-k஺2«a2-k

412⌱[Ýᙶ᪗ÌÞ!´<ᙶ᪗90,0,c,´☢9஽=X£´¤9A>0,c>0஺kᡠ@ß<x,y,zàáJx?+V+
z-c>=kz+—,kᓄᨵ/+y2+iX42Z2-2C
1+A0Z=0.
3@´☢9xOy☢´[9zHäå[Ýᙶ᪗Ì஺ᡠ@ß<x,y,zàáy]x2+y2=|z|,Vß<ÏÐ9/Xæ2=0.45[¹☢@ᩩ´[Ḅçᚖ9zH=çᚖèḄ<`çᚖᚖ[Ḅ☢9xOy☢[ᙠxQy☢Ḅᢗ[ḄÝᑖ9xHyHäå[Ýᙶ᪗ÌÞ![Ḅᔣᔣé9cosq,êsinq,஺ë[ᑖ'=<0,0,ì3஺ᡠ@ß222<x,y,zàá(x,j,z-^)x(cos^,-siny,0)=(x,j,z+^)x(cos^,siny,0),íî![(z-^)sinï2+[(-^)cos^]2+[xsið+ycosgz222222=[(z+—)sin—]2+[(z+—)cos-]2+[xsin--jcos22222ᓄ!xjsina=az஺᝞ò[£ᓽa=0,=,ᑣß<ÏÐ9☢z=0஺᝞ò[Øõᑣ஺=0,ᑣß<ÏÐ9Øõ☢xj=0.6.5ᳫ☢W+A+1=lḄX<,ᔣé஺PḄᔣö÷9A,ju,v
La2b2c2|ù=rúo:û=±+ᩩ+%.opᵫ⚪²!ᑮ

42r2//2r2v2HHÿ122v21=++,ᓽᨵMhF+h2227.ᵫᳫ☢5++[=1ḄOᩩᚖḄ!"#ᳫ☢ᑖ%&'abcᱏ,,P,,+|-|=.=1,2,3),123*+5+5=*+5+5.253+ᔣ7-(i=1,2,3)Ḅ:ᔣ;<=4,4,ᓃH=1,2,3),ᵫA⚪CDᨵE=G+£+G(I1,2,3).ᵫ'ᔣ704(1=1,2,3)KKᚖᡠMN▣Frabc14ᓃQ4஻2y2=S&N▣TUVW+4W+XW=+஻W+஻W=1,V3+VW+ZW=1.3஻3ᓃ_\U]ᑮ[+[+[=EF+*+4r2r3abe8.c#ᙊeᱥ☢10x2+2y2=zḄ&"=ᙊḄg☢஺i3T=ᙊeᱥ☢10*2+2V=%klmzo:ᔣ&"=ᙊᡠMg☢Ḅpᔣ7qrgs'xOyᙶ᪗☢v+ᡠcg☢=n3Ax+5y+z+D=0஺ᵫ'|}ḄᙊQ~ᳫ☢#g☢Ḅ&"ᡠMᙊv+=ᳫ☢x2+y2+z2+2ax+2by+2cz+d=0#g☢lḄ&"஺&"ᔣxOyᙶ᪗☢Ḅᢗ☢ḄUḄ:ᑖ%=10x2+2y2+Ax+By+D=0,(l+A2)x2+(l+B2)y2+2ABxy+2(AD+a-cA)x+2(BD+b—cB)y+D2—2cD+d=0,Ḅᦪ]ᑮ43=0,A='5=0,A=±2.g☢:3±2x+z=A஺102g☢⌕#ᙊeᱥ☢&g☢:ᙊeᱥ☢:]10-+2/±2*=4,:ᨵi:]ᑮA3k>--.

43⚪3.51.cᓫ☢+—=1A¢£2,3,-4Ḅ¤"஺222i3ᓫ☢¥+2QQ¥=1Ḅ¤"¦=4916«(—+[)+v(i+?)=o,w(-+-)+v(l-^)=O,243243(D<§(II).“_yஹ,xzஹ„w(l-^)+v(---)=0W(l+y)+V(y--)=O324£2,3,-4ᐭ¤"¦Ḅ:]ᑮ«IḄ®ᦪ=V=0,«IIḄ®ᦪ=஻+Z=0,ᡠM¢£2,3,-4Ḅ¤"=2x+z=0,fx-2=0,প°(n)±"3=0[4J+3Z=0.2.c"¦=²³=—ᡠ´ᡂḄ¶☢:஺21-1i3"¦7=·=3ᦋᑏ=x—XF=-2z+2,J—2=-Z4-1¼½;I®ᦪ]ᑮ¶☢:J2+z2+2jz-x-2j-4z+3=oO3.c#M¿"Àᐳ☢Ḅ"ᡠÂÃḄ☢fx=1fx=-lx-2v+1z+2z.15s[y=z[y=-za35—-3=—4=—5i3Ä⚪Åᡠc"ÆÀᙠ¢È4Ḅg☢Éᓽ“X1+'Z"¢£,:ᔣᔣ7=2,—஻Q஻Qy஺vx+l+y+z=0ᵫ'#4ᐳ☢ᡠM

44—11—v2—v2-u-v“Qv=0,ᓄÌ]ᑮ“v=-l஺"/Ḅ:Ḅ®ᦪÄÍᐵ¼½,-345]ᑮÏ"ÂÃḄ☢:x2+j2-z2=lo4.25ᓫ☢Ḅ¦ḄÐÅKᩩ¤"Ñ☢WѦḄÐÅKᩩ¤"ᐳ☢஺222253+ᓫ☢Ḅ:=Ò+¥QÓ=1(஺>0/>0,c>0).¤"¦=abcx=஺cosu+avsinu,x=acosu+avsinu,y=bsinu-bvcosw,§(HAy=bsinu-bvcosz=cv,z=QÔ(l)ᙠপÐÕKᩩ¤"12,ÖÆḄ®ᦪ=0K2V2×,/Ø஻2412ᑖ%¢£M(acosu,bsinw,,0)M(acosw,ftsinM,0):ᔣᔣ7xx222v=(asinu,—bcosuc)v=(asinu,—bcosw,c)ÙᯠK:ᔣqᐳ",ÛÜÝtxi9222ᔠßa(cosu-cosw)b(sinu-sin02t2(AfA/,v,v)=asinu-bcosuc1212xxasinu—bcosuc22=a6c[(cosu-cos6à+(sinu-sinu)2]22t=2abc(l—cos(஻2—%))/0.ᡠMপÐÅKᩩ¤"4,áÑ☢஺ᳮv](IDÐÅKᩩ¤"ãÑ☢஺(2)ᙠK¦¤"ᑖ%ÐÕQᩩä=ÖÆḄ®ᦪ=2V2×"],2ᑖ%¢£M(acos,ftsinWj,0)M{acosusinu,0):ᔣᔣ7x222%=(asinu,-bcosv=(asinu,-bcosu-c)஺x2229᝞è%="2ᵫ'¢Qé£ᡠM஺êᐳ☢஺᝞è/%ᑣÛÜÝᔠßa(cosu—cos%)b(sinu-sin%)22asin%-bcosuiasinu-bcosu22

45=—aZ>c[cos2„1—cos2u+sin2u—sin2w]=0,2x2ᡠMᐳ☢஺ìíî%=%+%À,4ágs஺5.+Sïð☢253(1)¦ḄÐÅKᩩ¤"Ñ☢W(2)ѦḄÐÅKᩩ¤"&W(3)¦Ḅᐰò¤"gs'Qég☢஺253+ïð☢Ḅ:=X=>஺•ḄK¦¤"=x=Q஻+OU,x=av+au^(D1y=bu-bv,O.(]1)«y=-bv+bu^z=2uvz=2vuyy(l)ᙠপ¦ÐÕKᩩ¤"4,4,ÖÆḄ®ᦪ=஻ö2ᑖ%¢£,÷(஺஻2)஻2°):ᔣᔣ7ᓃᓃ=(஻Qù2%)ÙᯠK:ᔣqᐳ"ÛÜÝᔠßa(u-Wj)b(u-MJ022(MlM2,vi,v2)=a-b2஻1=-4ab(u2—%ú*0.a-b2U2ᡠMপÐÅKᩩ¤"4,4Ñ☢஺ᳮv](II)ÐÅKᩩ¤"ãÑ☢஺(2)ᙠK¦¤"ᑖ%ÐÕQᩩä=ÖÆḄ®ᦪ=%024ᑖ%¢£M(av-bv0):ᔣᔣ7ᓃ=(஺,Qù2஻[),v=(a,Z>,2v)஺2292922ÙᯠK:ᔣqᐳ"ᓽqvûgs஺ÛÜÝᔠßa(v—W))—b(v4-Wj)022(MMvv)=a-b2u=0.l29l92lab2V2ᡠMѦḄÐÅKᩩ¤"Z],4&஺(3)ᵫ'(I)ÐŤ"Ḅ:ᔣᔣ7=ᓃ=(êQজ2஻),gs'g☢8x+ay=0,ᡠMপᡠᨵ¤"gs'g☢bx+ay=0oᵫ'(II)ÐŤ"Ḅ:ᔣᔣ7=v=(஺,2᜜,gs'g☢Bx—þ=0,ᡠM(II)2ᡠᨵ¤"gs'g☢bx-ay=0<>6.25ïð☢ḄS&¤"Ḅ&£ᙠQᩩ"A஺

46253+ïð☢Ḅ:=ÓQ5=2z,a>03>0.ᵫAQ⚪ḄCDïð☢Ḅ&ab¤"Q~ѦḄᡠMᙠপII¦ᑖ%⌱
:x-au+aVyx=av+auy(1)ீy(n)?☢z=ᓃAB•3ḄᩩEF
஺b2-a22z=27.IJ?☢ar++cz=Oa஻cK0L┵☢N+yz+zx=0Ḅ
<.ᩩḄ
PQ஺PQRIS┵☢*TUVV3=3.WXY3ᑮ┵☢Ḅ&
/4xzl—Ax+_y=0,4Ḅᔣᔣ—஺Zᡠ[&
ᙠ?☢y+kz=0.ax+by+cz=0(abcK0)h,ᡠᨵak+bk(k-1)+0(1—4)=0,ᓽ4+0஻CA+஺=0.Ḅ.]^_<ᡠ[&
Ḅ0ᦪᓰ,A2abb+c—ac+f=-----------=f—fb12bᵫ.ᩩ&
,ᡠkk+k#2k
l
k-1+1-^1-k
=0,c34t222ᐵ6dᐭᑮ£+£3+⁐=0,ᓽᨵ2+K+K=0஺bbbbabcg⚪3.6Lᵨjklm⊤nᵫoᑡ?☢ᡈF☢ᡠrᡂḄtuvwxyz{஺(1)x2+j2=16,z=x+4,z=0;(2)X2+16J2+9Z2=36,x2+j2+z2=16(ᙠ}Iᓶ▲ᑁ)஺

47^1/+y2=i6,z=x+4,z=0ᑖ<ᙊ☢.?☢⌕rᡂ]tuᨵvwᙠᙊ☢Ḅᑁ?☢z—x—4=0Ḅ?☢z=0Ḅ3!ᡠᵨjklm⊤>vwRx2+j2<16,z0.2ᵫᳫ☢x2+i6y2+%2=36᦮]ᙠᳫ☢“2+_/+஽2=16Ḅᑁᡠᙠ}Iᓶ▲ᑁrᡂḄvwᙠᳫ☢Ḅ᜜ᙠᳫ☢Ḅᑁᡠᵨjklm⊤>vwRX2+16J2+9Z2>36,x2+j2+z2<16,x>0,j>0,z>0.2.yᵫjklm04z<^8-x2-j2,0

48ḄᔣḄᙶ᪗Tᣚ§l<:cos®—sine]¬"]sin6cos®J|_vjᵫ⚪±JᔣAB=(-5,1)TWB'=(-1,5),<ᨵ-5]ªcoe-ssin^1.ᑮsine=U,cose=?.<'Ḅᙶ᪗Tᣚ§1J[sin®cos஺51313l

493yy-43.W¾ᙶ᪗6<¿Àᙶ᪗6'Ḅᙶ᪗Tᣚ§lV2,V2,cx=----xH------y+5,22ফᔆJ,(1)y=x-2.y=---x+—y-3ᐸx,_yLx',y‘ᑖ⊤>¯'Ḅ¾ᙶ᪗Lᙶ᪗[ᙶ᪗6Ḅ©'Ḅ¾ᙶ᪗x£[ᙶ᪗ÅÆḄ6஺^1ᙶ᪗6Ḅ©'Ḅ¾ᙶ᪗x'=0,y'=0dᐭ§lÇÈḄÉÊᓽ5,—3஺ᵫ'Ḅᙶ᪗Tᣚ§lJ⍝<¯ᔣḄ<Æ6absine=—»,cose=»ᵫ22lir046<2%ᡠ6=—.42L3Ì⚪¯ᳮᙶ᪗6Ḅ©'Ḅ¾ᙶ᪗2,3஺Æ8ab3Psin஺=-l,cos6=0,ᵫ0V6v2",ᡠ6=4.ᙠ¿Àᙶ᪗65W.
4Ax+Bj+G=0i=l2ÏÐᚖ¿¿Àᙶ᪗6ÑḄ஺᜛'O'x'Ô[Õᑮ5Ḅ'Ḅᙶ᪗Tᣚ§l஺^Rᵫ.
Ö4ÏÐᚖ£4,4¿Àᙶ᪗6ÑḄO'x'ᓽABi×Øᙠ¿Àᙶ᪗6ÙoḄ*"x'=o,4y'=o,ᡠÚ>0Ûcr24B,ᑮḄ'Ḅᙶ᪗Tᣚ§l:x~i2~+G)A+fiiy=(4*+ÜÑ+GCAÝÚ<0Ûaᑮ2Ḅ'Ḅᙶ᪗Tᣚ§l:24B2(Ax+5j+G),V=_-1,,(^2X+52y+c).2E+BQ

505.W஺46஺Þ☢ßàa2ᑮ?'Ḅᙶ᪗Tᣚ§l1-11X’11y'=-11ᔣḄᙶ᪗Tᣚ§l᪵஺z'112!A,5,C,øäùḄ?ᙶ᪗ᑖ

516.ᙠ¿Àᙶ᪗65={06],0203}ISá]ÏÐᚖḄ?☢n:x+y+z-1=0,n:x—z+1=0,II,:x—2y+z+2=o஺Ḅᙶ᪗6(2Õ=û஺'⍗,ý,.þÿ,
2,
3ᑖV°'z',z'O'x',x'ay'ᙶ᪗☢஺ᙠᙶ᪗Ḅᓶ▲ᑁᑮCT?ḄḄᙶ᪗ᣚ஺ᵫ!"☢
”
2,03ᑖy'0'z',z'o'x',x'oyᙶ᪗☢ᡠ%ᙶ᪗&'Ḅᐵ)*=±-y=(x+j+z-l),y'=±-j^(x-z+l),z'=±-j^(x-2y+z+2),+Oᙠᙶ᪗Ḅᓶ▲ᑁᡠ%஺ᙠᙶ᪗Ḅ!ᙶ᪗,-.x'=-*(x+y+Z-1),V=*(x-z+l),z'=-^(x-2y+z+2),ᦑ5ᑮa2ḄḄᙶ᪗ᣚ1R-X12ᕡ)0SZ21112S3,45V2V62--r0V3-7111"7372V67.ᙠ89:;ᙶ᪗஺?9x2-25y2+I6z2-24@+80x+60z=0⊤DEFG☢HI>?9x2-25y2+16124xz+80x+60z=0JKL>,(3x—4z)2—25j2+20(4x+3z)=0,ᵫ"☢3x—4z=0,j=0,4x+3z=0,MMᚖ:ᡠ%IOPᑖQᙶ᪗Ḅᙶ᪗"☢y'O'z',x'O'z',x'O'.Qᙶ᪗ᣚ

52=—(3x-4z),■y'=y,IOPRᐭ>?Tᑮx'2—y'2+4/o,UVW>?⊤DXGY=z=(4x+3z),ᱥ☢஺8.\]e_L“e|=1,Ir^e8_;`6T4,aᵨ⊤D4஺᝞deᵫe.ᓫgᔣie_Lr,ᡠ%/•^e8_;`lTᑮexr,ᔣir,20exrᐳ☢ᨵopḄqr./)⊤D/•sexrḄtឋvᔠᓽr=kr+lexrᑖsr,exrQᑁyTᑮz=cosg|=sin஺ᦑx஺=cosOr+sinOexr.▲jr9.I89:;ᙶ᪗s={0;%,02~3}^>ᔣv=(l,l,l)8_Tᙶ᪗er?={O;e,,e}5ᑮer2ḄḄᙶ᪗ᣚ஺ᐜὃ⇋!ᔣir^!ᔣiv8_6TᑮḄᔣiḄ⊤rḄQᚖ:vḄᔣi/•',^v8_஺TᑮḄᔣia',rḄ.Ḅ,.0'=coser'+sin6xr'./•'=•r'=r.->ᡠ%HM2H2

53r•vvx/*0=cos%+(1-cos6)—z-v+sin^..,MMᵫV⊤6«2«3^>ᔣV=(1,1,1)8_gTᑮe="e122,212J-JTS—CiH—e,d—=--e,H—€13τ3'ᡠ%ᙶ᪗ᣚ2-12122-1_zJ22ᓅz110.*s4.Mᩩᚖ:Ḅ☢:tᑖ8QM!oᚖ:Ḅ"☢tḄ.ᓫXG☢஺*☢:tḄ¡2aᜳ;2a,0?)⊤D[x+a=0,(x—a=09ீ,2<[y-ztana=0,1y+ztana=0,l.lḄ"☢«>?ᑖ2Jt(x+a)+j-ztana=0,Z(x-a)+j+ztana=0,⌕¥TM"☢ᚖ:ᑣᨵ(A,1,—tana)•(1,1,tana)=0,ᓽkl+1-tan2a=0,.o:tḄ®Ar/(x+a)(x—a)—(j—ztana)(j+ztana)=0,U(1-tan2a)x2+j2-z2tan2a=(l-tan2a)a2,ᡠ%tḄ.ᓫXG☢஺¯⚪4.31.ᑭᵨidᑡG☢Ḅ³ᓄ>?(1)llx2+10j2+6z2-12xy-8yz+4xz+72x-72y+36z+150=0;(2)x2+3y2+/+2xy+2yz+2xz-2x+4y+4z+1=0?(3)xy+yz+xz-a1=0;(4)9x2+4j2+4z2+12xy+8yz+12xz+4x+y+10z+l=0(5)2y24-4xz4-2x—4j+6z+5=0(1)µG☢Ḅ¶▣:

54¹ºiᱯ¼>?.½3+2722-1802+324=0,ᓽ(2-3)(2-6)(2-18)=0,ᱯ¼᪷4=3,/L=6,4=18,—=—12,213.³ᓄ>?3x,2+6y'2+18Z,2-12=0.ᓽx,2+2y,2+6z"-4=0.(2)µG☢Ḅ¶▣:ᱯ¼>?.-A3+542-42=0,ᓽ2(2-1)(2-4)=0,ᱯ¼᪷4=1,4=4,4=o,—=—ߟ=——,A42.³ᓄ>?x'2+4y'2±3j5z'=0.(3)µG☢Ḅ¶▣:

55022j_J_0A=2211022000¹ºi022£021020?1ᱯ¼>?./T+la+\=o,ᓽ(½1)(22+1)2=0,44ᱯ¼᪷4=1,4=4=—,Lt=—a2,23.³ᓄ>?x'2—y'2—2z'2=0.22(4)µG☢Ḅ¶▣9662£6442A=64522512¹ºi969644Z,=9+4+4=17,Z=£+246444

5696296196921+6833/=6445+4452~T,1251P22ᱯ¼>?.½3+17½2=0,49ᱯ¼᪷4=17,2=4=0,Á=2.³ᓄ>?17X"±7V=0.5µG☢Ḅ¶▣:0021020-2A=2003-235¹ºi000220++022000002002020-23020=-8,74=0.2003200-235ᱯ¼>?.13+222+4½8=,ᓽ422½+2=0,ᱯ¼᪷=4=2,4,=—2,4=0,*3.³ᓄ>?2x”+2y,2-2z2=0.ᓽx"+y,2-,2=0.z2.µG☢ᙊÄ☢ḄᩩÅ1=0,/=4/,Z=0஺324

57ᵨi⊤DḄᙊÄ☢Ḅ³ᓄ>?.A,x2+42y2+Æ=0.Ç=È=0,ᱯ¼>?%3+7,22-Z2=0ᨵM!o2pḄ᪷ᓽÊ/Z+A=0ᨵM!opḄ᪷U/=4A.3.a,b&Ë¥µG☢x2+j2—z2+2axz+2byz—2x—4j+2z=0⊤Dµ┵☢஺µ┵☢ḄiL஺஺Í=°ᡠ%10a-101-2,,I.==4a'+b'—4ab—2a—4Z>+4=0.4ab-11-1-2104.ÏG☢>?(ax+by+cz+d)(ax+by+cz+d=0ixxḄ³ᓄ>?஺*"☢f(x,y,z)=ax+by+cz+d=0f(x,y,z)=ax+by+cz+d=0lilliM"☢ḄÐᔣi஻=a,Òc,%=3”d%q,᝞ÓM"☢Ôᔠᑣ³ᓄ>?ax+by+cz+dp2x,2=0,ᐸ=x'=p᝞ÓM"☢"KÔᔠᑣ஻=a,b,c,஻i=ᐳtÖx%="+×+%+ÂØ+ÙÚ,nn%./(x,y,z)=|"|(x'+:(3y-d)),/i(x,y,z)=|஻i|(x'+%(Ù•)),ᡠ%2|«||«i|2|»,||«|³ᓄ>?AT2Ú=ÂÚ♦4|«||«1|᝞ÓM"☢"Kᑣ%OPḄ;"ᑖ☢ᙶ᪗☢~Üᙶ᪗ᓫgÐᔣiÝU;"ᑖ☢Ḅ>?

58+Þ(?*)=0,_.*%y)="OPḄÐᔣiᑖ.1«1pl«ll«i|஻°+஻,஻°஻஺ä!;"ᑖ☢y'O'z'☢è!;"ᑖ☢x‘O'z'☢UÖ1f(x,y,z)f(x,y,z)(}=PM-TT-,,_1(x,y,z)஻x,y,z)ஹy-|«°-<|

59\l«J.³ᓄ>?ñ1(|஻°+n»|2,2)=0,5.ᙠ:;ᙶ᪗஺ᑮz=⚔ᙠḄµ┵☢ax2+ay2+aZ2+2axy+2ayz+2axz=0u2233l223l3ᨵᩩoᚖ:Ḅ:õtḄᐙᑖ÷⌕ᩩÅ.a”+a+433=0஺22÷⌕ឋUµ┵☢Ḅ⚔ᨵᩩoᚖ:Ḅ:õtᡠ%⌱ýWᩩ:õtᙶ᪗()Ḅᙶ᪗¦ᙶ᪗dḄ>?a'x'2+ary'2'va'^z'2+2a\x'y'+la'^y'z'+2aJx/z=0n2223ᙶ᪗dḄ(1,0,0),(0,1,0),(0,0,1),ᙠG☢þ®ÿ☢Ḅᑮa1=0,Q2=°,*3=°'ᓽ/<=«+a+a—0.n2233ᐙᑖឋ#☢$%&┵☢ᡠ)*)⌱,〉.Ḅ/0ᙶ᪗34☢Ḅ$a2x,2+b2y'2-c2z'2=0,5I=a2+b2-c2=0,ᐸ7⌱8(c,0,a)ᓽ9/x:;<Ḅᔣᔣᑣᵫᔣ(—ab,J7E/c)HIḄ/:;(J/:;Kᚖ/஺Nᙠ)PQᩩ/:;#Sᙶ᪗3Ḅᙶ᪗Tx',y'TᙠUᙶ᪗3VḄ8(1,0,0),(0,1,0)ᙠ☢7ᡠ)☢Ḅ#a'''2+2a"'y'+2aJ'N'+2ax''z''=0,/I=஺1=0.ᵫU*^8(0,0,1)_ᙠ☢7`aIḄ/:;gJ/:;<ஹcdᚖ/ᦑ☢7ᨵgᩩhiᚖ/Ḅ/:;஺j⚪4.41.mVᑡ☢Ḅop(1)14x2+14y2+8z2-8xy-4xz-4yz+18x—18j+5=0;(2)5x2+26j2+10z2+6xy+14xz+4yz—8x—18j—10z+4=0;(3)x2+y2+z2—2xy+2xz-2yz—2x4-2j-2z-3=0.

60qr1s☢Ḅoptu14x—4y—2z+9=0,■—4x+14y—2z-9=0,Uvᨵw9q(9,,0)
ᓽ#op஺-2x—2y+8z=0,(2)☢Ḅoptu5x4-3j4-7z-4=0,x3x+26y+2z-9=0,`yz{|96y+2z+1=0,⊤~opᙠ/;ᓃllv+z+3=0,7x+2y+10z-5=0,1(3)☢ḄoptuX-J4-Z-1=O,«-x+y—஽+1=0,yz{X-Y+N—1=0
⊤~opᙠU☢7஺x-j+z-l=0,2.ᑨVᑡᔜ%&☢ὅ$op☢ὅ$op☢9ᑖ$;p☢ஹ☢p☢$p☢஺(1)3x2+5j2+3z2—4xy+2xz-2yz+2x+12y+lOz-F20=0;(2)2x2+18y2+8z2-12xy+24jz-Sxz—5x+15y+lOz+2=0;(3)4x2—j2—z2+2yz—8x—4j4-8z—2=0q(1)☢Ḅ▣x3-211-I3-21A=~25-16,/3=—25-1=29ᡈ(),☢$op☢஺1-1351-131652()J(2)☢Ḅ▣2-6-4--2152-6-41812T,<=-6512=0,ᡠ)☢$op125-41285152T☢஺☢Ḅoptu

6152x—6j—4z——=0,-6x+18y+12z+=0,vyz{94x+12y+8z+5=0,ᓽopᙠ9—4x+12y+8z+5=0,☢7ᡠ)$☢p☢஺(3)☢Ḅ▣00-4400-1-2,=A=0-11=0,☢$op☢☢1-14301-1-24-2optu4x—4=0,.9y+Z—2=0,vqᡠ)☢$p☢஺y-z+4=0,3.mVᑡᔜ%&☢Ḅ┵☢(1)2xz+j2-2z2—1=0;(2)x2+j2-FZ2-4xy-4xz-4yz-3=0;(3)5x2+9y2+92—12xy—6xz+12x—36z=0.Zqপ☢Ḅ001010=910,ᡠ)☢$op☢ᨵ┵☢☢Ḅop#8ᦑ30-2┵☢#2xz+y2_2z2=0.(2)☢Ḅoptux-2y-2z=0,92x+y-2z=0,8$`Ḅw9q☢$op☢ᦑ┵☢#—2x—2j+z=0,x2+y2+z2—4xj—4xz—4yz=0.(3)☢Ḅ5-6-3-690=0,ᡠ)☢$op☢Uᨵ┵☢஺-309

62j⚪4.51.mVᑡ%&☢Ḅ᜻ᔣ(1)9*2—4/—92+18ᑮ940yz-36=0;(2)x2+y2+4z2+2xy—4xz-4yz-4x-4y+8z=0q(1)☢Ḅ990Z=9-4920.0,ᡠ)☢ᨵ᜻ᔣ஺30-20-91(2)☢Ḅ11-2x+y-2z=0,11-2=0,ᡠ)☢ᨵ᜻ᔣ᜻ᔣtuvx+y—2z=0,yz-2-24-2x—2y+4z=0,x*+-22=0,ᡠ)¡{☢*+»—2஽=0Ḅᔣd$᜻ᔣ஺2.£¤☢x2+2y2-z2-2xy—2yz+2xz—4x—1=0mJᔣ1:(ߟ1):0ᐳ¦Ḅ/§☢஺q☢Ḅ▣1-11-2—12—10A=.Jᔣ1:(-1):0ᐳ⊈Ḅ/§☢1-1-10-200-1x—y+z—2—(—x+2y—z)=0ᓽ2x-3y+2z—2=0஺3.£¤☢4*2++z?+4©—4xz—2yz+x—y+1=0mª8Ḅ/§☢஺q☢Ḅ▣42-22~2ᑣJᔣxyzᐳ«Ḅ/§☢$01_1L22X(4x+2j-2z+-)+y(2x+j-z--)+Z(-2x-y+z)=0#¬ª822ᡠ)9!¥=0ᓽ=°±ᐭ/§☢Ḅoᑮ(392)(2*+»—#=0,ᵫ22U/§☢Ḅ2x+y-z=0.4.m☢S]:Jr?+>+z=o,S:x2+j2+z2-2x-2j-2z=0Ḅ³ᐳḄ/§☢஺2

63q#ᨵopḄ☢Ḅ/§☢d⌕¬ªopᡠ)mµ☢Ḅop¶*)qa·⚪஺s,x2+j+z=oJᔣxyzᐳ¦Ḅ/§☢Xx+1y+|z=o஺S2:*2+y2+z2-2x—2y—2z=oḄoptuvx—l=0j,-l=0z-l=0,ᓽop$1,1,1,op¸ᙠ/§☢7ᡠ)X+'y+,Z=0,ᦑ³ᐳḄ/§☢22$x-l=0.5.mVᑡ%&☢Ḅ¹ᔣJ¹§☢5mµ/0ᙶ᪗ᣚᑏµ¼ᓄ஺r1s14x2+14y2+8z2-4yz-4xz-8xy+18x-18j+5=0;(2)3x2+5y2+3z2—2xy+2xz-2yz+2x+12y+lOz+20=0.qr1s☢Ḅ▣…14-4|114-2+14-2,¿c=364=71H-28-28=396/=36,ᱯÁ$9V+3622-3962+362=0,ᓽ(2-6)(22-302+216)=0,ᱯÁ᪷$4=6,4=12,4=18.¼ᓄ$6x'2+12y'2+18z"—4=0.ᱯÁ᪷Ã=6Ḅ¹ᔣtuv8X-4K-2Z=0•94X+8F—2Z=0,ᑮ¹ᔣXy:Z=1:1:2,জÆ1,1,2)=()ǸḄ¹¬-2X-27+2Z=0☢$x+y+2z=0.ᱯÁ᪷;I2=12Ḅ¹ᔣtuv2X-4K-2Z=0—4X+2F-2Z=0,ᑮ¹ᔣXy:Z=1:1:(-1),ÉÆ1,1,-1)=0ǸḄ-2X-2K-4Z=0

64¹¬☢$x+y—z=O.ᱯÁ᪷4=18Ḅ¹ᔣtuv-4X-4K-2Z=0-4X-4K-2Z=0ᑮ¹ᔣX:஺Z=l:(-l):0,জÆ1,91,0)=18Ǹ-2X-2K-10Z=0Ḅ¹¬☢$x-y+l=0.☢Ḅop$1,9,rss/0ᙶ᪗ᣚ$2211Vfi>/3Ê111V6-\/3S2_1_0V6-\/32☢Ḅ▣3-14=11,4=:=364=36,ᱯÁ$943+1142-364+36=0,ᓽrË96Ì954+6=0,ᱯÁ᪷$4=2,4=3,4=6,¼ᓄ$2x"+3V2+6Z'2-1=0.ᱯÁ᪷Ã=2Ḅ¹ᔣtuvx-y+z=0,.9X+3V-Z=0,ᑮ¹ᔣX:y:Z=1:0:(-1),04(10-1)=-4ǸḄx-y+z=0¹¬☢$x—z-2=0.ᱯÁ᪷4=3Ḅ¹ᔣtuv

65-Y+Z=0,9X+2F-Z=0,ᑮ¹ᔣXzY:Z=1:1:1,o4111)=12ǸḄ¹¬☢x-y=0$x+y+z+4=0.ᱯÁ᪷%=6Ḅ¹ᔣtuv-3x-y+z=0,-x-y-z=o,ᑮ¹ᔣxyz=ir—2si,জÆ1-2,1=—6ǸḄ¹X-K-3Z=0¬☢$x—2y+z-1=0.☢Ḅop$r9,9W,_Us,/0ᙶ᪗ᣚ$636Ê#V6Ò313V273V6JL6.6.ÓÔªop☢ḄopḄÕ☢d$/§☢஺ÓÔÖop☢Ḅop#8ᑣª☢ḄopḄ☢#Ax+5y+Cz=0஺#op☢ḄH0,ᡠ)JÕᔣXy:Zᐳ×Ḅ/§☢ᙳÙᙠ*Ö#জ2ràá2s=45,ᨵw9qᓽÙᙠJᔣXyzᐳãḄ/§☢¶$ᡠäḄজ3rx,y,zs=Ac,7.åᑏµ%&;Ḅæஹ/§ஹ᜻ᔣஹᐳçᔣஹᐳè/§ஹÇéTஹ¹TJ¹ᔣḄIê஺qrᶍs8.ÓÔIᳮ4.5.2'஺ÓÔrᶍs9.ÓÔIᳮ4.5.3'஺ÓÔrᶍs10.m%&;5x2+5y2-6xy+18x-14y+9=0Ḅopஹ¹ᔣJ¹T஺

66q%&;Ḅoptuv:5x—3y+9=0,31ᨵw9q(_],)P¶$op஺—3x+5j-7=0,%&;Ḅ▣5-39A=-35-79-795-395-34=10,A=35=16஺°ð3=-35-7-162.ᱯÁ22-102+16=0,ᡠ)ᱯÁ᪷$4=2,ᮞ=8.ᱯÁ᪷#=2ǸḄ¹ᔣtu:3X-3Y=0,ᡠ)¹ᔣ#xy=1:1,জ«,1)=2,i¸Ḅ¹T$-3x+3y=0,32(x+y)+2=0,ᓽx+y+l=0.ᱯÁ᪷#=8ǸḄ¹ᔣtu:■=0,ᡠ)¹ᔣ#xy=l(T),জ3(1—1)=16,i¸Ḅ¹T$—3%—3=0,8(x-y)+16=0,ᓽx-y+2=0.11.£¤;©9-2x+3y-1=0Ḅ9ᩩ/§JyT¡஺mPᩩ/§Ḅ,mµ`Ḅᐳᱥ/§஺q;Ḅ▣$=2=9,*0,ᡠ)Õᔣ*¥dᨵᐳó214Y13Ḅ/§9x+(—X-y),+(-X+—y)=0.JyTx=0¡Ḅ/§¸tu222gx—y=o,ᓽxy=2i,ᡠ)/§$x=i,/§Ḅᔣ$xy=oi,J

67/§ᐳôḄ/§$õx—y+3=0,ᓽx—2y+3=0.22II.öªQ8(0,1)÷(1,0)Ḅ%&;F,)Q/;x-2y-l=02¥-y+l=0#ᐸ•Çᐳø/§mxḄ஺q#;ᐵ{/§ᙠᐸᐳᔣ7ᐹᨵÇéឋᡠ)᝞ý)ᐳþ/§#ÿᙶ᪗,ᑣḄax'2+by,2=c,ᵨᙶ᪗ᣚ[x=x-2y-l=0Ḅ,y'=2x—y+l=0,Ḅa(x-2y-1)2+b(2x—j+1)2=c,(0,1)(1,0)ᐭ!ᑣᨵ#$2-1)2+%-1+1)'!ᡠ)a(l-l)2+Z>(2+l)2=c,a=b,c=9aᦑᡠ+Ḅ,(x—2j—I)2+(2x—j+1)2=9.-⚪4.61.ᑏ56ᑡ89☢ᙠ<=ᜐḄᑗ@☢AḄB(1)x2+y2=z>(1,2,5);(2)I+F+z?—4xy—4xz—4yz+2x+2y+18=0,(1,2,3).F(1)(1,2,5)ᙠ☢*2+/=%!F(x,y,z)=x,F(x,y,z)=y,F(x,y,z)=--t23L(1,2,5)=1,ᡝ2(1,2,5)=2,N(1,2,5)=$ᑗ@☢,l(x-l)+2(y-2)-^(z-5)=0,ᓽ2x+4y-z-5=0.2A,—=ᓃ2=0.24-1(2)R(1,2,3)=—6,(1,2,3)Sᙠ☢!ᡠ)T(1,2,3)ᨵ☢Ḅᑗ┵!F(x,y,z)=x-2y-2z+l,F(x,y,z)=-2x+y-2z+l,l2F(x,y,z)=-2x-2y+z,iF,(1,2,3)=-8,F(l,2,3)=-5,F,(1,2,3)=-3,2ᑗ┵,[-8(x-1)-5(j-2)-3(z-3)]2+6[(x-1)2+(y-2)2+(z-3)2-4(x-1)(j-2)-4(x-l)(z-3)-4(j-2)(z-3)]=0,

68ᓽ70V+31y2+2++24XZ+6yz-324x-198y-126z+549=0.15Z56XY2.ᙠ☢“2+2»2+322+2W+2*஽+4*—8=+$!Y☢ᙠZḄᑗ@☢@[\$ᙶ᪗☢஺FBᑗ,^_!`⊟஺bᑣᑗ@☢,(x-X஺)F,(X,J,Z)+(J-J)F2(XOy>z)+(z-z„)F(x,y,z)=0000O003000(1)ᑗ@☢_y=0@[!ᑣᨵXo+Vo+Zo=0,■x+2yo+3z=0,Fc,(±2,+4,±2)஺00F(XoX”Zo)=0(2)ᑗ@☢_x=0@[!ᑣᨵ4+2d+2zo=0,•x+2yo+3z=0,Fc,(±4,+2,0)஺00.e(*0/0)=0,(3)ᑗ@☢_z=0@[!ᑣᨵX+X)+Zo=O,■10+2yo+2z0=0,Fc,(0±2f2g)஺.e(XoK)Zo)=O3.+_hi'=0'jx=0'ᑗḄkᳫ☢Ḅmnop!ᐸm!<=rᦪ஺z=a,1z=—a,FBᳫ☢Ḅᳫn,tu!=°'_ᳫ☢Ḅᑗ,^x”0,஺b!ᡎx=0,z=a,1z=-a,_ᳫ☢Ḅᑗ,0,y஺,$a஺i1'80'Ḅ{ᦪ,y=0,!r=0|}ᑗ!\z=a9z=a,{ᦪᐭᳫ☢mᨵ^/$/+£2+m2+3-஻b2=/,ᨵ᪷!ᑣx=lm2+a—n2=R2஺0yᳮ!cᑮy஺=/nJ?+m+஺hmR,ᨵ=0,,ᳫnopx2-y2+4az=0.4.ᳫ☢x?+y2+22+2x-4y+4z-4=0,+

69(1)T(1,5,4)Ḅᑗ@☢(2))(2,6,10)⚔Ḅᑗ┵☢஺F(1)(1,5,4)ᙠᳫ☢!i(x,y,z)=x+1,e2(xyz)=y-2᜛3(x,y,z)=z+2,L(1,5,4)=2,F(1,5,4)=3,e3(1,5,4)=6,ᑗ@☢,22(x-1)+3(y-5)4-6(z-4)=0,ᓽ2x+3y+6z-41=0.(2)—(2,6,10)=3,e2(2,6,10)=4,F(2,6,10)=12,F(2,6,10)=120,3ᡠ))(2,6,10)⚔Ḅᑗ┵☢,[3(x-2)+4(y—6)+12(z-10)]2-120[(x-2)2+(y-6)2+(z—10)2]=0.5.@☢18x+13j-2z+12=0_89☢x2+2y2+6xz+4yz+2y—4z+2=04ᑗ!+5ᑗᙶ᪗஺Bᑗ,(x°,yoZo)ᑣᑗ@☢,(x-x)(x+3z)+(j-J)(2J+2z+l)+(z-z)(3x+2y„-2)=000000000ᎷZ@☢,18x+13y-2z+12=0,U+3z0=2+2z(>+1=3*(,+2yo-2_-2%஺+24-18--13$=2-12Fcᑗ,(0,0,6),ᦑ@☢18x+13j$2z+12=0,89☢Ḅᑗ@☢஺6.+@☢ax+j3y—z+%=0_89☢Ax2+By2=2CzᑗḄᩩ஺FB89☢4/+62=2஺7Ḅᑗ@☢Ḅᑗ,(*0,ᓅ0),ᑣᑗ@☢,Axx+fijy=C(z+z)>,@☢ax+y—z+y=0!,ᨵoo,04==9=!ᓽᨵX஺=_!`=⊟஺=•(*஺!*஺)ᙠap\YAB☢!ᦑ=—2Cy,ᓽ¡+—+221=0.A.B2^,BC7.+89☢x2-3y2+z2-2=0ᐹᨵᔣ1:2:2ḄᑗḄop஺FBᐹᨵᔣ1:2:2Ḅix=X஺+£,,=¥+2f,z=&)+2E,_89☢X?—3y2+Z?—2=0ᑗ!ᑗ,(□”§)/))஺ᑗᐭ☢ᨵ(((x+£)2-3(j+2t)2+(z+2t)2-2=0000

70ᓽ$7R+(2x0-12+4z)f+x-+z-2=0,0ZḄ!ᨵ᪷!ᵫ(/Jo*஺),ᑗ!ᑣx—3y+z—2=0,,$7#+(2x0-12`+4z0W=0,24-12yo+4z0=0,©ᙠ%iḄmᢥᐵ¬/,⊟஺!cᑮ{ᦪ/Ḅᐵ¬B-7f=x—6y+2z,ᐭim!ᑣᨵ)6ᐵ¬Bx—6y+2z_8x-6y+2zX஺="+y=y2(x-6j4-2z)2x-5j+4z…+ߟ7—=$7$’2(x—6y+2z)2x—12j+llz4>=z+--------'--------=-------------------ᵫ(XoX),z஺)☢!ᡠ)¯ᑗḄop,(8x-6y+2z)2-3(2x-5J+4Z)2+(2x-12j+llz)2-98=0.°±²³ᣚᣚ-⚪5.11.ᣚḄ´A〉ᔠᔠ·!ᓽ(T,(<7,<7)=(CT,©,,)<7.33BO:SfS,i=l,2,3.,¸ᯠº,SḄᣚ!|»awS,ᨵூ<71(¿<73)](஺)=b'(cr2b=er,[

71cᑮᓽ@☢|iy=xḄÑÒB©=I"I.3.@☢i/Ḅ4x+6y+C=0,+@☢|i/ḄÑḄÒ஺FBᙠiÓᙶ᪗¬m!Px,yᐵi4*+_+஺=0Ḅ|Ô,Ø'^Ù',/b,ᑣP,P'Ḅmᙠi4*+Ḅ+஺=0!ÕÚe'_iᚖi!ᨵB£1££1Z=O,A+B+C<22ஹ^x'-x
B-y,-y
A=0,Fcᑮ@☢|iIḄÑḄÒB*=Ar+B2[^jg2-Ýx-2ABy-2AC],

72X=+I/-2),3ᐭi*+^-2=0mcᑮy=(/-2<+7)2/-_/-1=0.i*+§-2=0ᡂi2*-^-1=0.6.+@☢ḄᣚC>G«:HB9Ḅ⌮ᣚ஺35-3FBý▣A=Ḅ⌮ý▣,,ᵨA"4ÿ
ᣚḄᑮ:ஹ3-325-3VX5-3-32Ay+Vy)-3CH-3XH-3x,yx',y'ᣚᑮ⌮ᣚCH)(□ᡈ▣⊤!ᑏᡂ$%&Ḅ!'()x,yᵨx',y'⊤+,-᪵ᑮ/0஺7.ᙠ34ᙶ᪗78'9):☢<
Mo(x0,yo)=>஺4Ḅᣚ?!஺(@P(x,j)<
M(x,j)=>஺4AḄ
BP'(x',V),ᑣ000MP=(x-x,y-y),MP,=(x,-x,y,-y0),DE00000x—Xo)(cos஺—sin^Vx—Xfl>y-JoJ(sin஺cos஺J"FGHB:☢<
Mo(x0xJ=>஺4Ḅᣚ?!B:(x[(cos8—sin8)(x)[1—cos®ஹsin6cos8JyJ(-sin6k-8.JK:☢ḄMᔠB:☢Ḅ••PᣚQ஺JK:☢ḄMᔠRG஺ឤTᣚ/B4VW0Ḅ=>'ᡠY

73ឤTᣚ/GG஺@b”b2ᑖ[B4Ba,aḄ=>'ᑣcos&-sin^2Vx%5cosq9sin^\y\yJ2@](x,y),(5%)(P)BP'(x',V),ᑣcosq-sinq)(cos0-sin022sindcosJ|J^sin0,cos^2'cos(q+0)—sin(61+%))(x2ஹ5G(^+஺2)cos(^j+0)2ᡠYb1/4Bᵨ+bḄ=>'ᓽGG.@஺ᑖ[B4B6Ḅ=>'ᑣ>4RF6dᡈ2eF6Ḅ=>fBbḄ⌮ᣚ'DEo"TeG஺ᦑ:☢ḄMᔠB:☢ḄFPᣚQ஺9.JK:☢WhiḄMᔠB:☢ḄFPᣚQ஺JKᵫHhiB=>:kḄl'ᡠYឤTᣚ/+Bhi஺hiᙠ34ᙶ᪗7mḄ⊤?!B(n(cos0-sin6)(x)(a)UJ[sin®cosOJUJ+^JHB5b2Ḅ⊤?!B(cosa-sing)(cosgcr.cr,:,=''lᑓ[sinpcosg)(sin஺?cosq\r1*2Jl*i>(cos(^,+02)-sin(^+^2)V(cosW-sin^2Va2^16ஹ(simq+a)cos(p+g)J[yJ+ஹsin62cos^JUJ(b2

74DEl+Bhi஺@hibḄ⊤?!Bxr\(cos6-sin஺y\[sin஺cos6ᑣ()Ḅ⊤s!ᨵ:cos6sin9)(x')(cos0sin஺ஹusin஺cosG)\yf)(—sinCcos஺cos(-6)-sin(-^)V7ஹcos஺sin6)ua'sin(—6)cos(-6)usin஺cosGDEbᨵ⌮ᣚcos(-6)-sin(-^)Vx)(cos®sin^Va\CHஹsiii(-e)cos(-6)usingcos8r)ᦑ:☢WhiḄMᔠB:☢ḄFPᣚQ஺v⚪5.23XL:☢6=xx'y:kz=(2,-1),ᑏ)ᣚ?!'{9)
(0,1)஺2(:☢6=}Ḅᣚo;21:kM=(2,-1)Ḅᣚ~ᐜ6=-----y:kp=(2,-1),ᓽR~52HB
(0,1)EᣚAḄ
Ḅᙶ᪗B(3,-1)஺2.9
(3,1)ᡂ
(-1,3)Ḅ'{9)y2-x+8y+18=0E

75=>Ḅ஺(@:☢Ḅᣚb:[cos6-sin^Vx)Vj=(sineᵫH
(3,1)ᡂ
(-1,3)ᡠYcosg)—11(cos஺—(E$%ᑮsin6=l,cos=0,ᦑᣚB:3)(sine'ᓽx'=-y,y'=x஺j2-x+8j+18=0E=>Ḅ$%Bx'2—y'-8x'+18=0,ᓽ*2FF8"+18=0஺3.@ᣚbᙠ34ᙶ᪗7I8Ḅ?!R02交234ᙶ᪗ᣚ12পV31I229ᙠᙶ᪗78Ḅ?!஺(
P(x,y),]'(x',y')ᙠᙶ᪗78Ḅᙶ᪗ᑖ[RP(x,y),P(x',y')HBᨵYmᐵ7:ᐭᣚ?!8ᑮ:14▣22Ḅ⌮221,᦮ᳮᑮV31V32

76^673-2-72-3761_!6-+25▬Y6LfBᣚᙠᙶ᪗78Ḅ?!஺4.:☢WḄ
ᣚb34ᙶ᪗7Iᑮ34ᙶ᪗7II,{F
PᙠImḄᙶ᪗Ḅ]'ᙠnmḄᙶ᪗¡-'ᑣ஺Bᣚ஺JK@34ᙶ᪗7IR¢஺;6,02$
34ᙶ᪗7nR%O';e),e)$,{U1212,ᑣ¤¥▣A=B▣஺0=஺12
1+஺22,2
y@OP=xe+ye,O'P'=xye'=(ax+ay)e+(ax+ay)e.ᙠ3t22Xinxn2224ᙶ᪗7Im'O'P'=OP'-OO'=x'e+y'e-(ae+be)=(x'-a)e+(y'-b)e,HBᑮt2x2t2
ᣚᙠ34ᙶ᪗7ImḄᣚ?!§ᵪ+/)
ᦑ©
ᣚBᣚ஺

77=(¶Fº»+5F%)2=/(£,4).ᦑO■Bᣚ஺6.@¾¿ᑖ[B:☢WH3஺¿2ḄÀÁ'@Â4HO
'ᜳ4R6,JKr1B'>4R26஺JKY3ீRxÅ'O
Rᙶ᪗L
ÆÇ34ᙶ᪗7'@!(])=]',x2(]')=]"'ᵫHÊ¿஽ᑖ[B:☢WH34¿12ḄÀÁ'ᑣ\OP\=\OP'\=\OP"\,N(POP")=2aᡠYTTB4R26Ḅ=>஺2tE⚪+,Yᵨᑏ)ᣚ?!ᩭJK'ÍÎὅÐFÐ஺v⚪5.31.9Ñ
(0,0),(1,1)(1,—1)ᑖ[ᑮ
(2,3),(2,5),(3,7)ḄÒÁᣚ஺(@ÒÁᣚB«nÓᵪ+বÕ⚪Öᑮ஺=2,8=3,(YW$%&\a2la21J(3-1HBÒÁᣚB2.JKᙠÒÁᣚm'P×i
ḄØWF
ÙB×i
஺

78JK@]”ÛBÒÁᣚbḄP×i
'ᑣb(PJ=Ü,O•()=~.@b(O)=O'.r,ÛḄØWḄÝF
P,Þßà=Aὡ+(1F)â'ᑣ=a(OP)=ã+(1-t)OP^)=Q(+(1-t)a(OP^)=/ã+(1-1)ã=å'ᦑPP'æᔠ'ᓽPB×i
஺3.9Ñᩩ3x=O,x—J=O,J—1=0Õèᑮ3x—2y—3=0,x—1=0,4x-j-9=0ḄÒÁᣚḄ?!஺(3x=0,x-y=0Ḅ
BA(0,0),3x-2y—3=0,x-l=0Ḅ
BA'(l,0)X—y=0,»-1=0Ḅ
B8(1,1),*—1=0,4x-y-9=0Ḅ
B5”,F5)x=0,y—1=0Ḅ
BC(0,l),3x-2y—3=0,4x-y-9=0Ḅ
BC'(3,3)஺@ÒÁᣚḄ?!B3ᵪ+é),ᑣ"I,”஺,l«21a22AyJভ(YW$%&4.᝞ëFᩩ3ᙠÒÁᣚ7mḄæᔠ'ᑣìᩩ3R7Ḅ×i3஺9ÒÁᣚḄ×i3஺(@×i3B'4®+í+஺=0.ÒÁᣚᓤA3Ḅ$%ï,ᓄñRAx'+g'+C=0.ÒÁᣚTᐭAFP$%'ᑣᨵA(7x-J-1)+JB(4X+2J+4)+C=0,ᓽ(7A+48)x+(28-A)y+48-A+C=0

79HBòᙠᐵ7AB'Dó42+545+45?=0,ᑮA=-B,ᡈ7A+4B2B-A4B-A+CA=-45.\C514=-5,ᑣF=——------,ᦑC=—3,HBA:5:C=-[(-2):2:5],×i3B1:2x-2y-5=0.A=-4B,ôij-=——-——õijC=~B,HB×i3B64B-A+C5Z:20x-5j-8=0.öWᡠ÷'ÒÁᣚTḄ×i3ᨵᩩ/,:2x-2j-5=0,/:20x-5j-8=0.25.øᙊÑ+Ü=1¤ÒÁᣚTú2û2ᓄRx'2+y'2=l,ᵫEJKøᙊḄ☢l=ü஺1122JKÒÁᣚýḄl7ᦪB|detA|=ÿ>
ᙊ0ᓝ=1Ḅ☢S,ᙊabab~x'2+y'2=lḄ☢ᐔ&ᑣ=2ᦑᙊḄ☢S=nab.Sab6.O☢
᝞☢ᣚt•Oᢝ
!☢"MᑮM',$%&'OM'=kOM,ᐸ)
*ᦪA>0,ᑣ,T-./01ᡈ/03
,O4.0)5
6,4.07ᦪ஺1〉:⌱<᪗>
?@.0t■ḄBCD2EF.0GHᣚD3EF.0ᢝIJD4EF.0KLᑖNᡂPQRSḄT஺N1LO4UVWXIᙶ᪗7
Zx,y,ATx',y',ᵫ\51/=]^_
XᡠLx',y'=Ax,y,ᓽ.0fḄBC4knAk,ᵫ\*ᦪA>0,ᡠL4=K⌮,Qk0dᦑ.0GHᣚ஺

80(3)OMpOM2ḄᜳI6,ᵫ\*ᦪA>0,ᡠLf.0ᣚgḄᔣiḄᜳIjᯠ6஺(4)ᵫ\.0t■Ḅᣚl▣A=ᡠL.0_ᑖN4Q7.᝞☢Ḅᣚn
!opqrsḄtJuv4w*ᦪA,xτ,T4/0,,A4/07ᦪ஺(1)EF/0GHᣚD(2)EF/0yIzᑮ{u/0ḄyIzD(3)EF/0KLᑖNᡂw|ᣚ{.0ḄT஺EF}VWXIᙶ᪗7~஺;஺|V2
ᣚTᐳry4%
ᡂyP%,P%,P%,ᵫ\ᣚ1•pqrsḄtJuvw*ᦪA,ᡠL@ᑏ|:=A:>0(i#j).yP
,P%,P%Kᐳr,ᔲᑣ
P%,P%,P%ᐳr
ᑣᨵ▬1+11=11,M|+|2)=M஽|>y,Kᐳr,{Ꮇ
ᦑy஽',ᡭ
'Kᐳr஺ᣚᐳryP,P,PᡂᐳryP],PQ,PQ
t23+¡=@
ᑣ@¢+|”|=|ᓺd1஺\ᣚXrᡂXr஺ᵫL¥¦o@ᣚyIzᡂ{u/0ḄyIz஺(2)EF§¨஺(1)T(O)="HeJ=He?)=,ᑣ-|=:,1|,-=஺-,6_Le.©O'(a'b)e="%+%⁐
—a\ie\+a2ie2
(x,y)ᡂ஺12‘cos஺—sinffcosGsin0¬^=kᡈ4227\Sin6cosffsin஺cos஺ᵫ\ᣚyIzᡂ{u/0ḄyIz
ᡠLᎷZ(OP,e)=Z(O'P',e%),i=1,2,ᑣᨵᐵ7O-e,.==1,2,¬^i(x,y)(l,0)(7஺
/¯)(஺²”஺21)(x,y)(0,D_(x'-a,y'஻)(%2%஺22)´-µ⇼·´oA?%=ax,+ayf-aa-ab,k1y—axf4-ay,—aa-a22bᑏᡂl▣zCil2iu2in22l2

81\oᑮᣚᙠXIᙶ᪗7¹Ḅ⊤»zCcos6sin஺ᦑᣚGHᣚ஺(3)ᵫ\ᣚBCsin6)1X)eos஺—sin^Vkcos6jl0CMx}cos)\y)Hsin஺"x](cose-sine)(x\(a)ᡠL$KLᑖN4w|ᣚ(sine,{.0ᣚcos®ḄTTT,஺28.☢ḄGHᣚT!XrIḄÂÃÄ
r(A)=A',T(B)=B'.EF}(1)XrA5{A'B'ᡈὅ-ÇÈ\1,ᡈὅ/|\111஺(2)Xr44'{55'ÉÊÈ஺EF}(1)᝞A3{Xr/È(Ëᔠ)
^A'5’{/È
/|\
ᵫ\GHᣚz■!Xr/ḄÂÃÄ
ᑣPÄ
ÍᙠA5
ÎKḄ
ᡠL{
È஺᝞A5{Xr
/|
|\P,ᑣPÄ
¬^A'5'{
/|\஺(2)᝞45{Xr
È
ᙠ/

82åᯠ
ᣚ?•UᡂU
ᡠLKᣚBCᣚfᡂ1,0ᡂ1,0,ᡠLᨵᡃ%oᑮè2=a->a22=1,è1=°ᦑ┯ᑗḄBC4ᵫ\ᣚl▣ḄÈᑡCê\1,ᡠL┯ᑗᦋäzḄ☢஺ë⚪5.41.EF}ᙊḄᐳìXí{ᙊḄ|ᜐḄᑗr᪀ᡂḄÈðñzḄ☢*ᦪ஺EF}LᙊḄ)54U
tá
òá4xáÛyáVWXIᙶ᪗7
ᙊḄ¯óôGHᣚx'=n,y'=2,ᐸ7ᦪ2-
ᑣᙊᡂᓫ.ᙊ
-ÇᙊḄᐳabab᪽Xíᡂᓫ.ᙊḄᐳøXí
ᓫ.ᙊḄᐳùXíú/ᚖXḄ
|ᜐḄᑗr᪀ᡂḄÈðñzᡂw¯z
ᐸ☢44,ᡠL|ᜐḄᑗr᪀ᡂḄÈðñzḄ☢ᓅ4*ᦪ஺2.EF}ᙊḄ"᜜ᑗÈðñzḄQᩩpIrᡠᙠḄXrᙊḄpᐳÿ
஺ᣚᙊᡂᓫᙊᵫᑗᐳ
Ḅ!ᙊḄ᜜ᑗ#$%&'(%)'(%Ḅ*+ᙊḄ,-ᚖḄᐳ/
,12ᙊḄ3᜜ᑗ#$%Ḅ4ᩩ*+ᙊḄ•*ᐳΊ
஺3.:;Ḅᑗ<=Ḅ>?@AḄB+%Ḅ☢DEᦪ஺Gᙠ+ᙶ᪗KL:;Ḅ(MNW—Q=1,ᣚx'=B+T,y'=UTᐸDKᦪZᑣ:;Ḅ(a2bzabababMᡂX=1,xYZyY:;Ḅ4ᩩ>?஺22:;T3[\*0]^Ḅᑗ(My°x+Xoy=2,_`ᑖbcc஺ᡠeJoX஺

83ᑗ<=Ḅ>?@AḄB+%Ḅ☢Df=ᦑ:;£i=1Ḅᑗ2Jo*஺^b-<=Ḅ>?@AḄB+%Ḅ☢D2•k=abNEᦪ஺24.:;Ḅ4ᩩ>?lmḄᑗnoᑗ\pᑖ஺Gᙠ+ᙶ᪗KL:;Ḅ(MN^—■4=1,ᣚ7='+T4'='—Tᑣ:;Ḅ(Mᡂq=1,xabababYZjY:;Ḅ4ᩩ>?஺:;T3[\x,jḄᑗ(MJX+XJ=2,=<ᙶ᪗YḄr\ᑖb00OO2211—,0,0,—.=sḄt\ᙶ᪗uv-,v-^=x0,_y஺^ᡠe:;Ḅ4ᩩ>?lmJoX஺JoX஺Ḅᑗnoᑗ\pᑖ஺5.ᡠᨵᑁzᙊḄ#$%t☢DᨬᜧḄe*ᐳ
ZᙊḄr\N⚔\Ḅ#$%஺ᣚᙊᡂᓫᙊᵫᙊḄᑁz#$%t☢DᨬᜧḄ'(%)*+*,-ᚖḄᐳ
ᡠeᣚḄ⌮ᣚᑮᑁzᙊḄ#$%t☢DᨬᜧḄe*ᐳ
ZᙊḄr\N⚔\Ḅ#$%஺6.Lᑡᭆt%Ḅឋឋ1p$B+%2#$%3$%4B+%Ḅt5B+%Ḅ6ᙊḄ
஺%Ḅឋᨵp$B+%B+%ḄᙊḄ
஺%Ḅឋᨵ#$%$%B+%Ḅt஺7.᝞☢Ḅᣚz■ᙊᡂ=ᑣT'rᣚ஺eᙊḄᙊN\+ᙶ᪗KI=062ᵫ☢Ḅᣚt•ᙊᡂ=ᡠee6,02N(ᔣḄᐳΊ
ᡂᙊḄᐳ
ᔣe1,©2ᡂ,-ᚖḄᓫᔣe,+ᙶ᪗KI=0;%,02ᡂ+ᙶ᪗K11=00¡஺ᵫᣚ¢ᢝᔣḄឋᐵKᡠe3[\PᙠI=¥஺¦42tḄᙶ᪗<§\¨'ᙠn=O;e,¡tḄᙶ᪗-ª஺ᦑ«᪵Ḅᣚ&'rᣚ஺⚪5.51.L¯mḄ\ᣚ°±'rᣚ!²³Y஺

84ஹ'2_23-33ஹ11y=yfJ''14<-3723723V2J1Nᣚµ▣Ḅ·Ḅᔣᓫᔣ!44lm'rḄᡠeᣚµ▣¸'rµ▣஺ᣚµ▣Ḅᑡ¸p1,ᦑ»ᣚ°±Ḅ'rᣚ஺ᣚḄ4¹\Ḅº&³ஹY஺¼ᯠ\¹\¾²¹\ᓽ(MÀ2_21_ஹ3311y0y.x=3—2J5,y=J5—l,z=1ᡠeÁ''43V23Âyz_³Y(M3-272-V2-1-T'2.ᙠ+ᙶ᪗Kt²ÃÄ\(0,0,0),(0,1,0),(0,0,1)ᑖbᡂ\(0,0,0),(0,0,1),(1,0,0)Ḅ'rᣚŸ஺ᵫ\ᡂ\ᡠeÆGᣚŸa\\ya2iy.ᐸtᣚµ▣'rµ▣\ÇᐭᑮZ,2(MÀᑮa«=a=0,«=«,,=1,ᵫµ▣'rµ▣Æᑮ233332a”=%i=°஺21=±1ᡠeᡠ²'rᣚ001y±100y010Êzj3.Gcr¯mḄ°±Ḅ'rᣚ*¯mḄ3Ë4ᔣᓃ2ᨵপcr(v,)-cr(v)=Vj-v;22

85(2)cr(v)xcr(v)=o-(v,xv).122Ö×Ø+ᙶ᪗K1=[஺¦0]Ü3],°±'rᣚo■1=[0¦40203]ᡂ×Ø+ᙶ᪗K11=[0'¦0(4),<7(஺2),0(63)]஺G%ᙠ×Ø+ᙶ᪗KI=[O¦C],02,03]Ḅᙶ᪗N(/y1,è),(*2Ü)ᑣ(1)cr(v)-cr(v)={x^e^+ya(e)+z,cr(e))-(xo-(e)+ya(e)+za(e))12t23212223=xx+yy+zz=v-v.l2l2l2l2(2)ᵫb(e1)xb(e2)=b(e3)=b(e]Xe2),cr(e)x(r(e)=a(e)=a(exe),23l23

86ᐸᑡ0,ᦑ!ᣚ▣#⌮஺&'(ᙠ*+Ḅ-.!ᣚ/A!ᡂ1,i=1,2,3,4஺5.ᙠ-.!ᣚ3ᙠᐳ4Ḅ35ᡠᙠḄ6☢7Ḅ8+9'5஺:;<=A>,K'-.!ᣚbḄ@ᐳ4Ḅ5ᙠABḄ6☢ᑁDE+P,ᑣGDHḄOᡂIḄ!ᣚ᝞3

87y'=ycos20—zsin20,z'=ysin20+zcos20.ᵫᑮx1112Ḅt4z'!ᣚgY஺2Ḅ5᪀ᡂḄm4ᓽvwzuvwzvwḄn6☢ḄᜳnḄ2஺6☢.⚪6.11.=ᙠ᡽ᜧḄ¢£6☢74[3,—1,2],5[2,0,1],Q¤1¥m4A5ᙠ¦§ᙶ᪗iḄ¨©pqªᦪpq«¤2¥m4A57Ḅ¬®Ḅ¦§ᙶ᪗AᡠG¯Ḅªᦪ°஺Z¤1¥=m4pq஺ᵪ+஺2²2+%*3=°4[3,-1,2],5[2,0,1]ᙠm473a.—a,+2a,=0,\123Z/:஺2<%=1<¤+1¤+2,2a,+a=0,i233ᦑm4pq'x,-x-2X=0,23x=34+2஻xªᦪpq'vX=-2,2x=22+஻3¤2¥¸0=0,ᑣ¹="2,ᦑ¬®Ḅᙶ᪗'•G¯Ḅªᦪ°¼½1=34+v1=—ᡠ2=—1,஻=2.0=24+%2.:;<᡽ᜧḄ¢£6☢I7Ḅ@m4+%2=0,2¹+2+33=஺,5/+2X4-3x,=02ᐳ¿QÀḄ¦§ᙶ᪗஺

88X,+x=0,2X=ÂX:;<ᵫ&pqÃa2Ä+ᔛ+3%=0,ḄZ42”ᦑÆᨵ+ᐳX.=+ᓰ,5Xj+2X+3X=0,23È+1,1,1P.ᡠ@m4ᐳ஺3.ᙠ᡽ᜧḄ¢£6☢É7ÊËÌnḄ¢£m4ᙠ-.ᙶ᪗iḄpqQᵫAḄ.m4ᙠ¦§ᙶ᪗iḄpq¿QËA7☢Ḅ¬®<¤1¥x+2y—1=0;¤2¥x=0;¤3¥j=1;¤4¥3x—2y=0.Z<Íᐵ\x=2,y=@■Ïᐭm4ᙠ-.ᙶ᪗iḄpqi#ᑮs¯Ḅ.m4ᙠ*3“3¦§ᙶ᪗iḄpqᯠÒ¸6=0,Ó#ᑮ¬®Ḅᙶ᪗ᡠ¤1¥X,+2x-x=0,¬®Ḅᙶ᪗'23¤2¥1=0,¬®Ḅᙶ᪗'R0,1,0P.¤3¥X2—0=0%¬®Ḅᙶ᪗'È1%0%0P¤4¥3/+2஽=0,¬®Ḅᙶ᪗'R2,3,0P.⚪6.21.:;<.6☢7Õ@a>>ᐳ4ᑣ@4>Ö×ØÙ¹ᐳ.:;<=ÚRQ”¹6P/=1,2,3ᐳ4,ᑣm4K1>Ḅªᦪpq<01,2/3=431%஽,஺Û¥+஻Û¤42%2%஺2,m4ÜÙḄªᦪpq<¤ᱏ,²2%3=%¤Þß஺2+஻2஺3ß,3,m4P3PlḄªᦪpq<Xj,X,X=4஺3%%,%3+43%ß6.23m4à>Ḅ¦§ᙶ᪗'3”á6”4,â஺2=ãä%.m4P2P3Ḅ¦§ᙶ᪗'¤åß,஺2¥஺¤%ß,C3¥=VXV.23

89m44AḄ¦§ᙶ᪗'¤஺33஺3¥*31஽ᔩ¥=VXV3rᵫ&%xv,vxv,vxvj=2v,v,v
^0,ᡠ@4PR,P2P3,P3Plᐳ஺2233l232.@néA5CḄ⚔A,B,CᑖeᙠᐳḄ@m4'ëì7h5ABBCᑖe©ïPᑭ஺ñᑣC4ß©ïP஺7Ḅ+஺:;<ᙠ47DE+A'HA,òóA'tô&5'òó5'஺të&C'஺=AC4'஺'¹P஺ᑖet&R,R',ᑣA43c¹A4'3'C'¼½DesarguesᳮḄᩩ÷AC¹A'C'ḄtR”¹P,஺ᐳ4&'@R,R',R"øᔠᦑC4©ï7K஺Ḅ+஺3.@néABCḄú⚔A¹5ᑖeᙠm4147h5@ûAB,BC,CAᑖe©ïᐳ4Ḅü:⚔CḄýþ'+ᩩm4஺:;<ᙠm4ôë7E4',5'[Al'b'C'ÿA'5',5'C',CW
ᐳḄP,Q,RᑣAAfiCAA'5'C'Desargues⌮ᳮḄᩩAA',55',CC'ᐳᑣCC'4ᐳᓽ
஺Ḅ⚔஺Ḅᩩ
4,4ḄḄ஺4.!"☢$4Ḅ%&ᙶ᪗)*7”72,73+"=12,3,-4#4./஺0,4ᐳ2-324ᙠ6ᐰ)8Ḅ9ᦪ;<஻>%=A4+4%/=12,3../BC)/”0FᐳᡠHIᔣK*)72,73+"=12,3ᐳ☢஺ᵫ0஺0CMNᔣK*஻“P2,73+i=126ᐳᑣ*஻31Z2%3+W°Qᵫ*7,1P27,3+,=1,2ឋ⊤Fᓽ4ᙠ6ᐰ)8Ḅ9ᦪT%VA“+஻)/=1,2,3.XYZᯠ஺5.ᑏF]4⚪Ḅ_Ꮤa⚪஺bB!"☢$IὡḄ%&ᙶ᪗)%1%2%31=12,3,-ᡭ஺eᑣ஽hᐳ2-324ᙠ6ᐰ)8Ḅ9ᦪiI<">=k"+“2//=1,2,3.

90l⚪6.31.ᙠ!"☢fl$ᐳIA[1,2,5],5[1,O,3],C[-1,2,—1],ᙠ48$p஺>(A,5;஺,0)=5஺bBᵫᳮ6.3.1,஺[4ᑁ,F]-(4஻2஻3)=4(12,5)+஻(1,0,3)஺s(-1,2,-1)=(1,2,5)-2(1,0,3),ᑣ(A,5;C,Z))=5=(—2):tCMt=2,uvA,54=5,஻=-2,ᦑ(y,42/3)=6(1,2,5)—2(1,0,3)=(3,10,19),ᓽᙠA5$ᡠpḄ஺[3,10,19]஺2.ᙠ!"☢{ᓃ}~ᐳḄḄᙶ᪗4(2,-4),3(—4,5),C(4,-7),D(0,-l)pḄ(A,B;C,D),4121bBᵫ(4,-7)=§(2,-4)-§(-4,5),(0,-1)=§(2,—4)+§(-4,5),ᡠH(A,3;C,O)=(-4223.ᙠ!"☢{$ᐳ஺ḄI0FFḄ%&ᙶ᪗ᑖ)(10,3)(3,1,-4),(1,1,2),p
OḄᩩ4,>&,2“3"4)=—3஺b:0Ḅ%&ᙶ᪗3”%%)-(2%)=4(T°3)+M3,l,-4),s(1,1,2)=2(-1,0,3)4-(3,1,-4),ᑣ(Z,Z;/,/)=-3=-:^t=-4u;1=6,஻=1,0Ḅ%&ᙶ᪗I234)2A,X6(%,%,%)=(-9,-1,22),ᦑ1Ḅ9+x-22%=o஺424.A,5,C,0,EᐳḄ{-NN6./(A,B;C,D)(A,B;D,E)(A,B;E,C)=1./B+++ᑭᵨᳮ6.3.1,ᑣᨵ(A,B;C,D)=2:`,(A,B;D,E)=`:`,(A,B;E,C)=`:`,ᡠH(A,B;C,Z))(A,3;D,E)(4,b;E,C)=(K45.O6$Ḅ[F0ᐳ஺Ḅᩩ6./(635)஺

91./Buᩩ6
஺Ḅ/,/Z.=A,,(i=l,2,3,4)ᑣ(Z,ZiZ,Z)=(A,AiA,A)=441BV4£O1234I234&aA4A2ᵫI£¤AOA]A3%AOA3A2%AO4I44%AO44A2Ḅ¥AJAJ,AA,A,A,AA32442$Ḅ¦ᐭ¨Qᑮ(1i.//)=஺A4=_.ᐭ•A,(I2,3,4ߟ4A2•A&_&&•«44041O&sinN(AO&)஺᜜/ভ஺^)OA■OAsinZ.(AOA)OA-OAsinZ.(AOA)}2i24242sinN(A0A3)sinZ(AjOA)_sinZC/^/j)sinNQi/)4sinZ(AOA)sinZ(AOA)sinZ(/,Z)sinZ(Z,Z)324232426../Bᙠ®¯"☢$°}ᙊ$²6Ḅ³A],A2A3A4,ᑣᑮᙊ$²]{PḄ´Ḅ(””µ42µ43,µA,)ᦪPᙠᙊ$Ḅ¶·«ᐵ஺᝞ºµA»¼½ᔠ᝞ᑣᵨA4ᜐḄᑗÁÂ24஺./Bᵫ$⚪ḄÃÄᑮBஹsinN(A%)sinN(AM)(PA.,PA,;PA,,PA.)=----------!——:--------!———sinZ(AP4)sinZ(AjRA)3242s_ᙊᕜ$ḄÉP'ᡃᨵZA^'Aj=AA^Aj^iHj),ᡠH(PA,,PA;PA,PA)=(P'A1,P'A;P'A,P'A,)«2µ4»¼½ᔠÌᵨÍᜐ2i423ḄᑗÁÂÎᯠᨵ᪵Ḅ£ÐᐵÑᡠHÃÄÒᯠᡂÔ஺7.ᵫS,F\O,E(ᐸ»²I6ᐳ)<ᵫNN¨´ḄÖᩩ᪀ᡂḄؤÙÚÛᜓ¥¤(᝞ÝØ)஺./BNC,஺Þ<ᑖᒘNA,5஺

92s./BµESCḄ)H,ᐜáὃ⇋HS)»äḄåæH஺)»äḄåᡃᨵB(A,B;C,D)=(SA,SB;SC,SD)=(F,E;H,D),(F,E;H,D)=(OF,OE;OH,OD)=(B,A;C,D),CM(A,5;C,D)=(5,A;O,£>)஺ᑭᵨḄឋç(2),èij(A,fi;C,D)2=1,᝞º(A,5;C,O)=(ᡝ,E;H,0)=1,ᑭᵨḄឋç(3),ᑣᑮ(µ,0)=0,ìᓫ(᜛H,E)=0,CMµ=E,ïðñᩩòó஺ᡠH(A,5;C,O)=—LᦑNC,஺Þ<ᑖᒘNA,Bol⚪6.41../B!"☢$Ḅ!õᣚ÷õᡂ஺X]X]./B3”%,஺3)X2=0!õᣚ᜛x\=Ax2ᐸ▣AQ⌮Ḅ஺õᡂ(øù2஺3)47X=0,Îᯠ⊤úᩩ஺2.pF÷û(1)(஺V1+ax+ax)2±(ý"[+bx+ftx)2=0,22332233(2)(ax+ax4-ax)(6x+bx-+-bx)=0,i12233112233õᡂ{!þYḄ!õᣚ஺b(1)᝞º=S”)2)3)Aÿ±1
஺]0,ᑣ

93px\=ax+ax+a,x,,ii22px=X2PX3=*ᓄp2l±k2
x^=0,ᓽᨵ=00᝞31,02஺32஻3
ᐳᑣpx\=a,x,+ax+ax,2233aal222-px'=bx+bx+bx,0,ᓄPx\±᳾=0,ᓽ2i{2233ab2px'=x,33X%3X%=03.ᙠ!☢#$%&'(=0,x=0,x=0ᑖ*+'23ax+bx+஺-3=஺,/=1,2,3
Ḅ+ᣚ஺j1i223ᡠ$Ḅ+ᣚ5=Ax,ᐸ▣A56⌮Ḅ▣AḄ⌮▣5A-1=/%-஺ᵫ;<ᩩ>?ᑮஹ(1,0,0)84-1x=(al,bx,cl)x\,1,0)22A*2=(“2”2஺2)*2-3,(0,0,1)஺,’PiᡠB0ᦑ+ᣚ5

94bPx02b20Pib*00D⚪6.51.ᙠ!☢#FGHIJA[l,—1,0],5[2,0,-1],C[0,2,-1],D[l,4,-2],E[2,3,—2],$ᵫKLᡠMNḄOP஺23OPḄ5a,,x^+a,,x+a„x1++2a,x.x,+=0,xQHIJḄᙶ᪗Tᐭ?ᑮ஽11+஺22—^^12=0W11+033Xᵲ3=/v.22+/3-4a23=°a+16^22+4஺33+.12Xộ13—16a=0,n234a+9\+4%+12a—8^.,—12a,=0,ttor92?]?=஺23=—=஺12_5OPḄ514I/?I/7ZZ1Z7111Z2x+2x+lx஺\+40r.x+9x«x,+9xx,=0o1Z?Z?J2.$JPl,2,1ᐵ_OPa3x—x+x—25“2—4(*3=0Ḅc᩽஺T-1-2ஹ23OPfḄ▣5X1—10ᡠBJe1,2,1ᐵ_OPfḄc᩽5g201,1210ᓽ3/+3h+“3=03.ij3k⌨ᓄOPḄm/nᨵḄoḄc᩽5pqr'஺ij3smOtuX'/wOPx_yJA,B,஺5A5ḄJz{Oᐵ_A,5Ḅ|}J5'#ḄpqrJ_5k⌨ᓄOPḄm/nᨵḄoḄc᩽5pqr'஺4.ᎷNT5ᙊ┵tX'/#ḄXJA,uJAᐵ_rḄc᩽஻Kx/_J5,J5Ḅc᩽x'_J஺sA஺᪵ᡃLu%A5C,KḄ

955⚔JḄc᩽Ic᩽஺ij3᝞'(=(),“=0,“3=0uc᩽Ḅᙊ┵fḄQᨵ3ax,+Px\+yx\=0.ij35஺,4஺,45Ḅᑖ*5(=0,*2=஺,*3=0z3஺5JAḄc᩽ᡠB5CḄa\\ai2ai3X](100)ai2%2a23x=0>ᓽax+ax+«x=0&_52111l22133ஹ“13a23433”3,%2=3=0ᳮ?ᑮ62=஺23=0஺z{ᙊ┵]ḄQᨵ3ax]+Px\+yxj=0.5.ij3ᙊ┵ᯖJḄc᩽5஺ij3ᙠ¡!☢#X'ᙶ᪗¢£?ᙊ┵Ḅ5᪗B¤ᱥ¦,{§“2=2¨ᯖJ5(0,᝕)5ª=X«஺_5ᯖJḄc᩽5ᓽPW+¬=0Kᙠ'ᙶ᪗¢Ḅ25ª=',®¯5஺6.ᵨ±²³ᵫt´JSuᙊ┵Ḅᑗ(᝞±¶)3'1}'25t´uḄ,ᐸ·Ḅ'᪷¹¶Ḅº»¼½u%'8}'9¯5ᑗ¾j¿u³Ḅᳮᵫ஺ij3ᵫD⚪6.3ḄÀ7⚪<⍝'1,2w'7ḄxJᑖ*5'1,2wᙊ┵ḄxJJSḄÀ4|}Jz{'75JSḄ᩽'7wᙊ┵ḄxJ®ᙠJSḄ᩽ᓃÃÄyxJḄ᩽®sJS஺ÄᓃḄJḄ᩽5ᑗᡠB'8,9¯5ᑗ஺

967.ij3Å#ḄpqrJḄc᩽5KḄÆÇÃÄÅ#pqrJḄᑗ5ÆÇ஺ij3zÅḄmḄ᩽5pqr'ᡠBpqrJḄ᩽sm஺zÅ#ḄpqrJḄ᩽sKÈᡠB᩽Ḅᔣ5ÆÊᔣ_5᩽5ÆÇ஺˳3Å5*—=0,ᑣpqrJ51,±1,0,ÆÇ5x,±x=0opqrJ1,±1,0Ḅ᩽52’10(1±10)0-1=0BPxt+x2=0•ᡠBÅ#ḄpqrJḄஹ00c᩽5KḄÆÇ஺