2022-2023学年北京市某中学高二10月月考数学试卷含详解

《2022-2023学年北京市某中学高二10月月考数学试卷含详解》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。

ᓝᓝᨴᨴὃᦪᔁ2022.10.9ஹ⌱⚪1.ᔠ={1235,7,11},84|"#"15#<஺},ᑣAgᐗ*Ḅ,ᦪ-#"A.2B.3C.4D.52.12aeR,"l+ai#i=3+i,"i-9ᦪᓫ;#ᑣ஺="#A.-1B.1C.-3D.33.12=஻?@ᩩBCḄDE஺£?@,BCḄG☢IJKᑡM,N⚪Oজ᝞RSua,nua,m///3,n//3,UVS7஻Wঝ᝞Rmlln,஻_La,UVWঞ᝞Ra_L஻mua,nu0,UVm±nWট᝞Ranᨴ=஻`஻2_L஻஻ua,UV஻_L/?ᐸdeN⚪Ḅ,ᦪᨵ"#A.4,B.3,C.2,D.1,4.gᦪ/"x#=2sinGyx+e#"O,lel<3#Ḅnᑖpq᝞pᡠsᑣḄt-"#5.12Buᙳ-ᓫ;ᔣx"22+u#."225#=-yᑣz{BḄᜳ}-"#A.30°B.45°C.135°D.150°6.ᦪz|z-3+4i|=lᑣ|z—2Ḅᨬᜧt?"

1A.V4T+1B.V17+1C.V15+1D.VB+I7.஺ᙳ-┦}tanacos/?—sin/?=1,ᑣ"#JTA.+J3=7iB.2a+/3=—C.3a-(3=RD.2a—/?=]128.12+=1,ᑣJḄᨬt-()abA.y/2B.272C.4D.8”ஹax-b9.gᦪ/(')=;——3Ḅpq᝞pᡠsᑣKᑡᡂḄ?()(x+c/A.a>0,b<0,c>0B.a<0,b<0,c>0D.a<0,b>0,c>010.᝞pᙠdz஺-☢ḄP-ᡠᙠḄM,N-dzḄ⚔.ᑣজঝB.ঝঞC.জঞটD.ঝঞট11.12dzA5CO-4ᱏ£஺|£-2,P-¤¥.K

2AD—1——ᑡ¦deḄ?(A.AP=QA2,ᑣ§☢DE3P{G஺ᡠᡂ}Ḅ©ªt-33B.Bᡝ=%83+5(/16[0,1]),°┵P-ABC²B?tC.zᡝ=286+38³(/le[0,1]),ᨵ´ᨵ,µ¶G☢AB/D.Aᡝ=4ADW(/le[0,l]),ᑣ§☢DE8P·CQᡠᡂ}¹t»?ஹ⚪12.12ᦪzi=3+i(i-9ᦪᓫ;)ᑣ¼=.13.gᦪ/(x)=lg(l-4sin2%)Ḅ½¾-.14.ᙠAABC}A,B,CḄ¿ÀᑖÁ-a,"c,bcosC+ccos8=a2,Æ=JJ,AABCḄ☢²-ᑣ஺Ḅt-215.£,5-ÈÉᔣxᑣ?"Ê+)=Ë-Ì”ḄᩩÍ.16.᝞pᙠGÎMÀÏA8CDAB=BD=DC=1,AD=BC=6ÐGÎMÀÏABC஺Ñ¿}E8஺ᢚᡂ°┵A—BCD,µG☢A8D_LG☢6C஺ᙠKᑡ:

3AA'জDECDG☢ABDWঝG☢ABC_LG☢BCDWঞBC{A஺ᡂ}Ḅᜧ-45°;টA'CÔÕᙠᑮ⚔A'ஹBஹCஹ஺Ḅ×ØÙÚ;ঠBᑮG☢AC஺Ḅ×Ø-Û4ᡠᨵdeḄÝÞ?.x2-1>«17.gᦪ/(x)=<gᦪ/(x)Õᙠᨬtᑣ஺Ḅ,¹t-a\x-3-a\+3a^

4õö¶ᑮOB_LOC,÷஺ᙠøÀABÔ.(1)ßùOG☢COZ)G☢AOBO(2)஺-4BḄß☢}6—C£>—OḄ©ªt;21.᝞pᙠ°ûABC-44GAABC-ÚÀ°}ÏMÀÏBCC4?À£-2ḄdzÏ஺-AB(1)ßùO஺஺G☢48ᨴ4W(2)ᙠEügcÔDEAP{G☢4஺஺ᡠᡂ}Ḅdªt-¦ßᑮG☢4஺஺Ḅ×5Ø.22.᝞pᙠ°ûABC—4AGMÀÏAAGC?À£-4ḄýÏAB=BC=^ஹD!"ACÔ÷(B{A,Cþᔠ)G☢ᵨ8஺4GE.BB/IDE}AF)Q(2)=ᩩজஹᩩঝஹᩩঞᩩ⌱"#ᩩ$%&'()*AB-☢AC4ᵨBOEᡠᡂ3Ḅ567.ᩩজ-☢ABC1-☢A4CCᩩঝ/4AC=60?ᩩঞ:48=?.

523AB"ᦪᑡ{஺“}IJᦪp,MN+p>0,«,+p=0ঝV/ieN*,%

6ঞ᝞¬a_L/?,Zua,nu(3ÀÁmVn-,ট᝞¬aPl=ZmLn,஻ua,ÀÁ஻_LÇ.ᐸ5ɼ⚪ḄᦪᨵÊËA.4B.3C.2D.1ூᫀ௃Dூ᪆௃ூᑖ᪆௃᪷ÍÎÏ**ஹ*☢ஹ☢☢Ḅ¦ÐᐵÒ}}ᑨÔᓽ_.ூ௃Iজ᝞¬mua,஻ua,ml13,n///3,ÀÁÕ஻஻ᡈZ"®ᦑজ┯ØIঝ᝞¬m஻"n±a,ᵫ*☢ᚖ)ḄឋÛ_'஻z_L஺ᦑঝ5ÉIঞ᝞¬a_L£,mua,஻u£,ÀÁZ_L஻ᡈm//஻ᡈZ஻®Êrᚖ)ËᡈZ஻Ü☢Êrᚖ)Ëᦑঞ┯ØIট᝞¬஺Ý£=஻bmln,“ua,ÀÁ“ᡈ஻ᨴ®Êrᚖ)ËÞßàÞa/?,a[\P=m,Ln,஻ua,ÀÁ஻J_/7,ᦑট┯Ø.mᦑ⌱D4.âᦪ/ÊxË=2sinÊf9x+eËÊ3>0,lel<^ËḄæᑖçè᝞çᡠéᑣḄ7%ÊËB.6D.1ூᫀ௃Bூ᪆௃çk.ூᑖ᪆௃ᐜ᪷ÍâᦪḄçè(oâᦪḄ᪆/ÊxË=2sinê(ë/ஹ57r7124ூ௃ᵫç_kT=2—--=ᐔ=--69=2,12I127CO

7ᵫç_k2sinÊ2x1|+᜛1=2,ñভ<],஺=}ÊᡠY/ÊxË=2sinÊ2%}஺Ë“ᙍ=2sin12x/}ᓣsᦑ⌱B.5.&'45ᙳ%ᓫ¦ᔣøÊ2M+B>m-2BË=-úû,ᑣ45Ḅᜳ3%ÊË2A.30°B.45°C.135°D.150°ூᫀ௃Aூ᪆௃ூᑖ᪆௃ᵫᦪøþḄÿ
£,ᯠᵫᦪḄ
ᜳ
ᜳᜧ.ூ௃2஺+஺"•—2஺"=———>(•2a2-3a-b-2b2=-^.2•+a,5ᙳ+ᓫ-ᔣ
,2=/=1.—3a-bߟߟ3"
ab--r@a•r=21஽35Ḅᜳ+eᑣcos஺aUU9ᔠ6e[0,>],
஺=30஺.ᦑ⌱CA.6.EFᦪzHI|z—3+4i|=lNOU|z-2|ḄᨬᜧS"A.a+1B.V17+1C.V15+1D.V13+1ூZᫀ௃Bூ᪆௃ூᑖ᪆௃12=^+"`>6/?",
cx,y"Ḅfghijᑭᵨ|z—2]Ḅmno9ᔠᙊḄmnឋr
st2|Ḅᨬᜧ.ூ௃12=u+”%,y€/?",ᑣz-3+4i|=|(x-3)+(y+4)i|=^(x-3)2+(^+4)2=1

8ᡠ}FᦪzᙠF☢ᑁḄcḄfghi+(x—3)2+(y+4)2=l,ᙊ(x-3y+(y+4)2=lḄᙊᙶ᪗+(3,T),+1|z—2|=J(X-2)2+/⊤ᙊ(X—3)2+(y+4஺=1scᑮc(2,0)Ḅ|z—2|Ḅᨬᜧ+7(3-2)21+(-4-0)2+1=717+1.ᦑ⌱CB7.14ᨴᙳ+┦tanacos/?-sin/?=l,ᑣ()JTA.3஺+£=ᐔB.2a+4=5C.3a-/3=nD.2a—/=tூZᫀ௃Dூ᪆௃ூᑖ᪆௃9ᔠ¢£¤ᦪḄ¥¦ᐵ¨©ஹ«¬Ḅ®©ஹ¯°®©
±Zᫀ.ூ௃²⚪oC£ᙳ+┦tanacos´—sin஻=l,sina°-aஹsinacos'-cosasinᨴ■cosf3~sin஺-1,-1,cosacosasinacos(3-cosasin(3=cosa,ᐔsin(a-/)=sin--a22222ᐔ71ᡠ}a—/7=w—a,2at᜛>.ᦑ⌱CD128.a>0*>0,t+—=1,ᑣ஻஻Ḅᨬ+()abA.V2B.2V2C.4D.8ூZᫀ௃Dூ᪆௃ூᑖ᪆௃ᵫ¥¦µ©¶·
.ூ௃ᵫ¥¦µ©
2¸¹º‘+2=1,᦮ᳮ
¾?28Vabab121EEs=C=L,ᓽ஺=2,=4Nᡂ.ah2

9ᡠ}¾?Ḅᨬ+8.ᦑ⌱CD,/ஹax-b9.¤ᦪ/(x)=EḄÂÃ᝞ÂᡠᑣÅᑡ9ÇtᡂḄS()«>0,b<0,c>0B,a<0,b<0,c>0D.«<0,/?>0,c>0ூZᫀ௃Aூ᪆௃ᑖ᪆௃ᑭᵨᱯËÌcj9ᔠ¤ᦪÂÃᓽ
ᑮZᫀ.ூ௃ᵫÂC஻0)=W>0,ᡠ}b<0,CEᡝ-cN¤ᦪ“X)ÒoᵫÂCt஺<0,ᡠ}c>0.AbÓ/(x)=0,
x=2,ᵫÂCt<0,aaÔ+6<0,ᡠ}a>0.ÕsCa>0,b<0,c>0-ᦑ⌱CA10.᝞ÂᙠhÖ×஺+Ø☢Ḅ×P+ᡠᙠÚḄ×cM,N+hÖḄ⚔cᔓHIᵨN஺ÞḄS(M1(D

10NA.জঝB.ঝঞC.Q)©টD.ঝঞটூZᫀ௃Bூ᪆௃ூᑖ᪆௃1hÖḄÚ+2,᝞Âãäå¶ᙶ᪗¨ᑖæ¾çè⌱⚗×Ḅᙶ᪗ê
ë3ëḄᙶ᪗ᑨíîh=0Sᔲᡂê
±⌱⚗.ூ௃1hÖḄÚ+2,ã᝞ÂᡠḄäå¶ᙶ᪗¨CðজCᵫÂC"(2,0,2),N(0,2,2),0(1,1,0),P(0,2,l),ᡠ}ñ=(-2,2,0),OP=(-1,1,1),+ò.=Tx(_2)+lx2+0=4/0,ᡠ}ë3µᚖ¶ᓽMN_LOPµᡂᦑজµ±(ðঝCᵫÂCM(2,0,0)N(0,0,2),0(1,1,0),´(2,0,1),ᡠ}ộ=(t2,0,2),ë=(1,-1,1),+ñë=lx(-2)+0+lx2=0,ᡠ}ë3ᡠᚖ¶ᓽMN_LOP,ᦑঝ±(ðঞCᵫÂ:M[2,2,2),N(0,2,0),0(1,1,0),´(0,0,1),ᡠ}ộ=(-2,0,-2),OP=(-1,-1,1),+ò.ë=—lx(-2)+0+lx(-2)=0,ᡠ}᪗73öᚖ¶ᓽMVJ.OP,ᦑঞ±(ðটCᵫÂCM(0,2,0),N(0,0,2),0(1,1,0),P(2,l,2),ᡠ}ë=(0,-2,2),=(1,0,2),+ëë=0+0+2x2=44ᡠ}ë3µᚖ¶ᓽᵨNJ.QPµᡂᦑটµ±(ᡠ}ঝঞ±ᦑ⌱CB.

1111.hÖÚ+2,P+äå×tc.ÅᑡÇ÷±ḄS"ᑣø☢¶ù8´3C|OᡠᡂḄ+3B.ᑖᡝ=2ᑖû+üý4e[0þ]",£Ú┵—ABCḄC.ᡝ=/Li^+g8/te[0/Dᨵ"#ᨵ$%&'(AC1*☢AB/D.ZA=/lAD./le[0,lDᑣ1☢23BP5G஺ᡠᡂ:;=>?ூAᫀ௃DூD᪆௃

12ூᑖ᪆௃A>G4?H&IJ3P,8£,6஺E,஺ᑖK8G,80H&IJ஺LMNOᑮ1☢23BPQG஺ᡠᡂ:G/OEAᡈᐸ⊡:UᐸVW.B>PᙠYZ&[\]^LPBC☢ឤ4ᑮ☢PBCḄ`aឤᓽcᑨe.C>fᔆᑖKB4CC1H&pᙠEFYZ&[\]^hi4cl☢AM஺᧕k⌕'4cl☢ABFᑣmᙠ☢A8Qᑁᓽcᑨe.D᪀pqr2:ᙶ᪗uv0,a,2-a
,ae[0,2],wᵨᔣzᜳ:Ḅᙶ᪗⊤}Ucosீ,ுᑨeᜳ:Ḅ$1----=.ூD௃A>ᵫAP=/AQ,ᓽPGA?H&12BP,BgBD,E,OᑖKBQ,8஺H&IJ0E,EQ,ᑣ஺E//G஺,3BE=PDஹ4BE//PD1,ᓽBE஺/G*ᡠ6BP//EQ,ᡠ1☢238QG஺ᡠᡂ:ᓽG/OEQᡈᐸ⊡:OE=OG=eED[=7,OD,=76,ᦑcos/O£஻=2+g—=,┯;2B?\sj6B>ᵫᓽ=4+4e[0][k>ᙠᵨGYZ&[\]^᝞}P8C☢ឤAᑮ☢P8CḄ`aឤᦑP-ABCḄ┯;C>ᑖK,CC1H&ᵫ=2+gẬe[0,1]
k>PᙠEFYZ&[\]^,

13ᵫCO1☢A£>4ACDu☢0c4,ᑣ☢AOA4☢஺C4ᵫAD1\D,☢c☢OCA,=4஺tᡠAA1☢OCA,ACu☢DC&ᑣADJ\C,ᳮch>ABJ.AC,ttᵫAQcAg=A,AD.AB|U☢A8Q,ᦑ4cl☢A8Q,]☢AgPc☢AgQ=Ag,⌕'ACS☢AB/,ᑣmᙠ☢A8Qᑁ¡ᯠaU☢A8Q,ᦑ┯.D>ᵫAA=/lAO.(/le[0/Dk>PᙠA?(YZ&)\]^᝞puGQ,2,0),0(0,2,2),5(2,0,2),ᑣᵬ=($2,0,2),vP(0,a,2-a),ae[0,2],ᑣBP=(-2,a,-a),ᡠcosᓽ¦"¨©ªᢚ¬2—஺re[0,2],--------_TT®஺=2,ᓽ¯=0°cos=0,±°233P5G஺ᡠᡂ:².

141Icos>=—®஺³2,ᓽxe(0,2]°ᑣ26,+412<6(1—´+.2Xxx3311----------ஹ²ᐔ®$=/=ᓽ஺=0°cosDூ&½௃ᐵ¿&&½>᪷ÁᔣzḄ3ឋᐵuᑨePḄÃÄÅᔠ1☢23ᜳ:ḄÇஹ┵ÉÊஹ3☢ᚖ2ḄᑨÌᔣzᜳ:Ḅᙶ᪗UÍhiᡈUD3☢ᚖ2ஹஹ1☢23ᜳ:=Î.ªஹÏq⚪12.NkÑᦪzi=3+iiGÓᦪᓫÃ[ᑣூAᫀ௃VioூD᪆௃ூᑖ᪆௃ᑭᵨÑᦪḄ◀ÍᓄØÑᦪz,ᑭᵨᐳᵗÑᦪḄÇÅᔠÑᦪḄÛÜÉÊcU(ÅÝ.ூD௃ᵫ⚪Þc(2=9=ᓃt=1—3i,ᑣ=1+33à±á=Jâ+32=ᮞ.ᦑAᫀG>M.13.äᦪ/å=✂1-42ὡḄÇèG.ூAᫀ௃^——+k7r,—+k7r^,keZூD᪆௃ூᑖ᪆௃᪷ÁéᦪḄêᦪᜧë0,DÎÊᓽc(ìAᫀ.1?TTTTூD௃ᵫ⚪Þ(>1—4sin?X,஺ᡠ—-k+Z»w+Z"J'ZEZ14.ᙠABCH:A,8,CḄéᑖKG,"஺cosC+ccosB==ôABCḄ☢GB,ᑣCḄG.2ூAᫀ௃2ூD᪆௃ூᑖ᪆௃ᑭᵨºWᳮᓄ:c(“ᵫ:☢ÉÊc(C,ᯠMᵫö÷ᳮc(.(D௃ᵫºWᳮc(sinBcosC+sinCcosB=sin(8+C)=sinA=asinA

15àAE(O,஻)sinA>0,ᡠ஺=1úS=—ctbsinC=QûLᡠsinC=lARC4ABe222rr--------------úàGCe(O,ü)ᡠCM,,ᡠc=J7ý=J17^=2ᦑAᫀG>215.v£,᙮
ᔣᑣ+q=-Ḅ__________ᩩ.ூᫀ௃ᐙ⌕ூ᪆௃ூᑖ᪆௃ᑭᵨᑖᐙᑖឋ!⌕ឋᑖ"ᑨ$ᓽ&.ூ'(௃ᐙᑖឋ)*2_LBᡠ/7B=O.*4+஻=[a+b\-a+2a-h+h-a+b,\a—b\=(a-b\-a-2ab+b-a+b,ᡠ/,+=67q2,ᓽ,+0=6-q.ᦑᐙᑖឋ9:)!⌕ឋ)*;+4=67ὡᡠ/6+,=,—>?஻+஻={a+b\-a+2a-h+h,஻7஻--a—2a-b+b,ᡠ/7+27B+ᱏ=7727B+7,ᡠ/4£4=0,ᓽ£4=0,ᡠ/Aᦑ!⌕ឋ9:.ᡠ/“CD”“B+q=B-q”Ḅᐙ⌕ᩩ.ᦑᫀ)ᐙ⌕.16.᝞GᙠIJKLABCOAB=BD=DC=1,AD=BC=O,MIJKLA8CDNOPQ8஺ᢚᡂUV┵A—BQD,X☢A8D_L☢BC஺ᙠZᑡ\])জ_QCD_L☢A6D`ঝ☢ABCJ■☢BCD)

16ঞ6cdA£
ᡂPḄᜧC45°;টVA'Cghᙠ7iᑮ⚔i4ஹBஹCஹ஺Ḅmnop`ঠiBᑮ☢ACDḄmn—`4ᡠᨵst\]Ḅuv.ூᫀ௃জঝটூ(᪆௃ூᑖ᪆௃ᑭᵨ☢☢ᚖ_Ḅឋx&ᑨ$জḄsy`ᑭᵨ☢☢ᚖ_Ḅᑨᳮ&ᑨ$ঝḄsy`ᑭᵨ_PUPLḄ{|ឋx&ᑨ$টḄsy`/i8ᙶ᪗iDCஹ7Ḅᔣᑖ"xஹVஹzḄsᔣ_Pᙶ᪗ᑭᵨᔣ&ᑨ$ঞঠḄsy.ூ'(௃Oজ*30=8=1BC=6,ᑣ802+82=8஺2,ᡠ/BDVCD,••☢ABD☢BCD,☢A'BD஺☢BCD=BD,CDu☢BCD,ᡠ/CO_L☢AজO`OঝvA'B=BD=lA'D=6,ᑣAB?+BO2=AB?ᑣA'3_L3£>☢A6£>,A'8u☢ABDᑣAB_LC஺•.•8஺8=஺.•.A'8_L☢BCD•.•A'6u☢A'BC,ᦑ☢ABC☢BCD,ঝO`/i8ᙶ᪗iDCBDᵬḄᔣᑖ"XஹyஹzḄsᔣ᝞ZGᡠḄ_PᙶᑣA(O,O,l)ஹ3(0,0,0)ஹC(l,l,0),£>(0,1,0),OঞBC=(l,l,0),=(0,1,—1),cosI>=,42,ᡠ/_Q8CdA'DᡂPḄᜧC67ঞ┯;Oট*☢ABD,A£u☢4BDᑣCC4'஺ᳮA3_LBC,

17ᡠ/QA'CḄiᑮ⚔iA'ஹBஹCஹOḄmnopটO;Oঠ^0=(0,1,-1),=(1,0,0),=(0,0,1),n-A!D=)v--z=0*☢Ac஺Ḅᔣ஻=(x,y,z),ᑣ<7'¢y=l,ᑣ”=(0,1,1),ᡠ/i8ᑮn-DC=x=0ஹ'\BA.'-A10L--L=-=^-.ঠ┯•☢A'COḄmndFrrMO2ᦑᫀ)জঝট.2117.¦ᦪ/(x)=<\x-3-a\+3a^aூᑖ᪆௃ᓄ±஻x)=<,ᑖ²³]´ᣵ¶O¬·v,¸?ᑖ²³]஺Ḅ¢¬ºt|x-3-a|+3a^Kafx2-lrr>tzூ'(௃ᵫ⚪¿Äf(x)=<.τ|Ç—3—+3a,x0Èa=0É/(x)=Ê7Ë+3»x<0ᑣxNOÉ/(x)e[-l,+oo),%<0É/(X)G(3,+OO)ÌÉf(x)hᙠᨬC¬-1,ᦑaḄ7¢¬0`ঝÈa>0ÉᑣxNaÉ/(%)ᙠ3+8)gᓫÐ⌴Ò/(%)e[a2-l,+oo)x-l,ᓽa2—§,ᑣ7§Wa<0`

184ÕgᡠÖaḄ¢¬º4],ᑣaḄ7¢¬0`஺ᨬᜧ¬4,ᦑᫀ)0`4.Uஹ(⚪18.¦ᦪ/(%)=Üᐸᔣa=(2cosx,l),b=(cosx,A/3sin2x+m).(1)æᦪ/(x)ḄᨬCsᕜæ(2)஻ç)ᙠ[0,&gḄᓫÐ⌴Òé`ব¨Èxe0,[É“X)Ḅᨬᜧ¬4,Ô?Ḅ¬.ூᫀ௃(1)ᐔ`(2)[0,—],[ߟ,7t]`63(3)m=1.ூ(᪆௃ூᑖ᪆௃(1)ᵫᦪôᙶ᪗⊤ÃÄö@),øᑭᵨùúPûÂஹüPḄsýûÂᓄ±¦ᦪÂ,ᯠÿᵫ
ᦪឋᨬ
ᕜ(2)ᵫ
ᦪḄᓫឋᓫ(3)ᵫ
ᦪឋᦪᨬᜧᦪ.ூ1"#௃ᵫ%&/(%)=2cos2X+A/3sin2x+m=cos2x+V3sin2x+m+1=2(^y-sin2x+cos2x)+m+lit=2sin(2x+—)+m+1,2ᐔᡠ9ᨬ
ᕜ:7=3=ᐔூ2"#௃TT7T7T7T2kjt—W2x+—W2E+—,ku—192
`ᩩbজdᓃf஺=1ᩩbঝdᓃcos4=ijkᩩb[l⌱fknIᩩbcosBoaḄ.ூp2ᫀ[r1
A=SᡈA=t332
⌱ᩩbজdcosB=,a=7E⌱ᩩbঝdcosB=—,a=7.714ூ#᪆௃ூᑖ᪆௃r1
ᐜᵨ
yᳮ{|Ajr2
⌱ᩩbজdᐜᑨ~{4=—,ᑖ{cosCஹsinCஹcosAஹsinA,ᑭᵨj|oḄᓽ{3cosB,ᵨyᳮ{aTT⌱ᩩbঝdᐜᑨ~{4=—,ᑖ{cosCஹsinCஹcosAஹsinA,ᑭᵨj|oḄᓽ{3cos5,ᵨ
yᳮ{a.ூ1"#௃ABC[IcosC=f,ᡠ9sinC=Ji-cos?C=14ᵫ
yᳮda=———ᡠ9sinA=@sin஺=2'ᒹ=^.sinAsmCc3142ᡠ9A=SᡈA=22.33ூ2"#௃⌱ᩩbজdb—a=1,ᑣ%ᡠ9A=2rA=^.33]3Q1FxQcosC=—,sinC=——»cosA=—sinA=—,f141422131]ᡠ9cosB=-cos(4+C)=—cosAcosC+sinAsinC=----x—+------x=——v71421427ᓽcosB=--7ᵫyᳮdb1-cr+c2-laccosB-f7#d஺=7஺=f.⌱ᩩbঝdbcosA=--.2

20I>0,ᡠ9cosA<0,ᡠ9A=Z^A=.ᓃQcosC="sinC=-331414c°sA=Tsi"=322_13"+x3=Uᡠ9cosB=-cosrA+C=-cosAcosC+sinAsinC=X-14,214214,an5----2-x---ᵫ
yᳮd——=——ᓽb.cosA..sinAsinfi-xsinAA^2^^xsinAsinBsinB5G7TBPa=l.20.᝞ᙠ4஺6[ZAOB=90°,AO=2,O8=1.2\AOC9“9AOI¡¢ᑮ¤OB_LOC,¥¦஺ᙠ§¨AB©.r1ªd«☢COZ
J_«☢408r2
P஺IA8Ḅ[¦Q☢|Ḅ;ூpᫀ௃r1pᫀ®#᪆ফG5ூ#᪆௃ூᑖ᪆௃r1
᪷°¡¢±ᱯឋ³ᑮNAOC=90°,ᯠµª¶OCJ•«☢A08,ᨬµª¶☢☢ᚖ.2
᪷°⚪º»¼t|ᙶ᪗³ᑮ¿ᔣÁᵨᐵÃ☢|ḄᔣÁÄÅᓽ.ூ1"#௃□AAOC9^AOB9AOI¡¢ᑮ□NAOC=90°,ᓽOC_L஺!

21DOCLOB,OAu«☢AOB,OBu«☢A08,OBcOA=OOC,«☢408,¤OCu«☢CO஺□«☢COO_L«☢A08ூ2"#௃᝞»¼9஺Iᙶ᪗ͦ0CᡠᙠIx08ᡠᙠI04ᡠᙠIzḄt|ᙶ8(0,1,0),C(l,0,0),£)(0,-,1),0(0,0,0),2—Ïߟ1—1BC=(1,-1,O),CD=(9D=(0,-,l)Ò«☢Be஺Ḅ¿ᔣÁIᓃ=r3,y,ZÓ.BC=X]-x=01—.1ÒÔ=2,ᑣÔ=2,Z]=1,ᦑ/=(2,2,1)I1f%+—%+4=0ஹ2Ò«☢COOḄ¿ᔣÁI“2=rS2%22%CD=-x+—y+z=02222ÒÖ=2ᑣw=0Z2=-1,ᦑI2=(஺,2,—1)n.OD=—y+z=0222cos=TA-=-f=~~MN,☢|5—CD—OḄIÚᑄM•P5521.᝞ᙠÜÝABC-4ÞG[A3CIà¨|áT¨áBOQᱏ:¨äI2Ḅ
åáD!

22AA3[¦¤=æ./fè........(1)ªdCQL«☢AB4A(2)é¦PᙠP\yBBiëqc©¤APí«☢4c஺ᡠᡂ|Ḅ
Iï¦pᑮ«☢4஺஺Ḅñò.ூpᫀ௃(1)ª¶®#᪆(2)R5ூ#᪆௃ூᑖ᪆௃(1)ᵫóôyᳮª¶4ALA஺ᵫAAL8C,ª4A«☢ABC,ᓽCCA4fᵫC£>_LAB,ªCD_L«☢A844(2)ᵫ⚪ºª¶஺4,஺ö஺஺jjᚖ»¼t|ᙶ᪗÷ᑏ{ùú¦Ḅᙶ᪗íᔣÁḄᙶ᪗#«☢4C஺Ḅ¿ᔣÁÒCP=X=(24240),/1e[0,1],ᵫᔣÁᜳ|ḄüᐭÄÅCP=(1,1,0),᪷°¦ᑮ«☢ḄñòüᐭÄÅpᫀ.ூ1"#௃ª¶dᵫ⚪&AA=2,45=1,4஺=æAD2+M=5=ÿ=A/_LA஺8181BC4B஻4A,ᡠ4ALBC,3ADC\BC=B,AZ>,BCu☢ABC,ᡠ4A_L☢ABC,C£)u☢ABC,ᡠᙠAABC஺A3CD1A8,A3cAA=A,48,#U☢AB4AᡠCDJ•☢ABB14ூ()2+,௃.BC஺,4GQᑣOA±BC,OQ±BC,ᵫ(1)4AA☢ABC,5OAu☢A8C,ᡠ஺4_14313஻AA,ᡠ஺4_L3g,34cBe=8,BBSBCuT☢BCqBI

23ᡠQ4_L☢8CC4,஺4,OB,0Q99ᚖ;.᝞>0ᙶ᪗ABCDḄFᔣxHஹyHஹzHḄFᔣJKLM;Nᙶ᪗Oᑣ0P0,0,0Q,AP0,0,V3QAP0,2,x/3Q,CP-l,0,0
,DE,0,V,4120Q,ᡠ8=R=1,2,যT=(2,2,0),AC=(-l,0,-V3).U☢A஺஺ḄVᔣW3=x,y,z
,3n-CD^Q-X+ᑣXᓽீ2TYZ=0x+2y+y/3z=0]x=l,ᑣz=—_,y=l,஻=(1,1,`_aUC=Xb=(24,240),c«0,1],ᑣd=យ+C=យ+4T=gh_1,2/1-G).ᵫ;iAPj☢\CDᡠᡂNḄlmR,5•cos,Cn|=_______|2"1+2ஹ+3|________=2^5_"ஹ''q717m4(24-1)2+3)2+3—5ᓽ|2/l+l|=J(2/l—l)2+(2/l)2+3᦮ᳮt4Z2-82+3=0ᵫᡠu=ὡ,F=/1T=1,1,0Q.\CP-n\|11|2Y+UPᑮ☢Ḅxydᑣz=`^|=`/!!-ᔁ,ᡠᑮ☢4஺஺ḄxyWV1+1+352.

24ூ௃FVKuNḄ)⚪ᑭᵨLMᔣWV,☢ḄVᔣWᑭᵨᔣWḄᜳN,.22.᝞>ᙠABC-ABJGAAG஺4ḄA8=BC=஺ACPjA,C¡ᔠQ☢ᵨ8஺jAC£E.A\EG1
¤BBJ/DE/BADaP2Q¥F=¦§ᩩ©জஹᩩ©ঝஹᩩ©ঞ®ᩩ©⌱°9®ᩩ©±²4;iABj☢ᡠᡂNḄlm.ᩩ©জ☢A3C1☢AAQC³ᩩ©ঝ/AAC=6஺´³ᩩ©ঞ48=µ.ூ¶ᫀ௃P1
¤#¸,᪆³ফ—.13ூ,᪆௃ூᑖ᪆௃P1
ᵫḄឋ½t/^//ᔧ¿ᓽtᑮBBJ/☢ACC4,À᪷Âi☢ÃḄឋ½¤#ᓽ³P2
⌱জঝÄÅ4C,.AC஺ÄÅ4஺B0,ᓽtᑮA01AC,᪷Â☢☢ᚖ;Ḅឋ½tᑮA஺Æ☢4BCᓽtᑮA஺Æ஺8,Àᵫ301AC,ᓽJKLM;Nᙶ᪗OᑭᵨLMᔣWVÇi☢NḄlm³⌱ঝঞÄÅ4C,.AC0,ÄÅ4஺B0,È⚪Ét4஺1AC,ÀᵫÊËÌᳮ⌮ÌᳮtᑮA.O1OB,ᓽtᑮA஺S☢A8C,ÎÏÐজঝ³⌱জঞ.AC0,ÄÅ80,4஺ᓽtᑮ801ACᵫ☢☢ᚖ;Ḅឋ½tᑮ801☢ACC.A,§Ctᑮ8஺Ñ஺A,ÀᵫÊËÌᳮ⌮ÌᳮtᑮA஺1A஺ÎÏÐজঝ³ூ()1+,௃

25ᙠABC—AAGA4,/!BB,84Ò☢AC£AA41U☢ACC4,]ᡠ8ᱏ//☢AC0A☢ὡBDEc☢ACGA=஺E^ᱏÒ☢_lÇᡠ6BBJ/DE.ூ()2+,௃⌱জঝÄÅAC,.AC஺ÄÅ4஺B0.ᙠACGANAAC=60?,ᡠAAACÔN.஺ACᡠAQ1AC,☢ABCJ.☢ACG4☢ABCc☢ACCiA=AC4஺Ò☢4஺஺[4ᡠ4஺1☢ABC,OBu☢ABC,ᦑ4஺1஺8,3AB=BC,ᡠ801AC.஺A஺8ஹocஹ஺4xHஹyHஹzHJKLM;Nᙶ᪗Oᑣ0(0,0,0),A(0,-2,0),A(0,0,2g)3(3,0,0),0(0,1,0).ᡠ×(`3],0),DE=M=(0,2,2V3).n-BD=-3x,+y=0ᔆU☢4BOEḄ`®VᔣW஻=(X1,y,z),ᑣØ___,\Z[=_<3,ᦑa=(1,3,—Ú).ᐗ.£)E=2y+2Î=0—ABn\9UUUC=(3,2,0),U;iA8j☢ᱏ8/ÜᡠᡂN6,Ýijsine=|cos(A8,Þ■.ᡠ;iAS1Ð13

269j☢BஹBDEᡠᡂNḄlm—.⌱ঝঞÄÅ4C,.AC஺ÄÅ4஺B0ᙠACG4/AAC=60?,ᡠAAACÔN.஺ACᦑA01AC,5§0=2603=3,4Ç=ᔊ.ᡠ402+032=432,ᑣ4஺Ñ08.ACcOB=O,AC,03u☢ABC,ᡠA஺1☢A8CᵫOBu☢ABC,ᦑ3AB=BCᡠB01AC.஺A஺8ஹocஹ஺4xHஹyHஹzHJKLM;Nᙶ᪗Oᑣ0(0,0,0),40,-2,0),4(0,0,26)B(3,0,0),D(O,1,O).ᡠd=(`3,1,0),á=â=(0,2,2_)._

27-BD=-3ã1+ä=0ᔆU☢Ḅ`®VᔣW஻=(X],y,zJ,ᑣå_l]Z]=-GᦑY=(1,3,-6).[n-DE=2j+2V3z=0l1uiuI—■IIAB,“948=(3,2,0),U;iABj☢ᡠᡂN஺ᑣsin6=|cos<48,Y)|.τæ,Ð139ᡠ;iABj☢B.BDEᡠᡂNḄlmm.⌱জঞ.AC0,ÄÅ80,4஺.ᙠAABCç84=BC,ᡠ8O1AC,5AO=2,08=3.☢ABCJ.☢ACC௃A,☢ABCc☢ACC]A=AC80u☢ABC,ᡠBOI☢ACGAC%U☢ACGAᡠ6஺1஺4.ᙠRt/OA஺4,=26஺4=2,M=4,ᡠ042+042=éᑣ401Ao.ᵫ6OcAO=O,BQAOu☢ABCᑣ☢ABCᵫ08u☢ABC,ᦑ4஺1஺8,3AB=BC,ᡠ801AC.஺AOBஹOCஹ஺4xHஹyHஹZHJKLM;Nᙶ᪗Oᑣ0(0,0,0),40,—2,0),4(0,0,273),8(3,0,0),

28ê0,1,0
.ᡠd=P`3,1,0
,á=â=P0,2,2_Q._

29-BD=-3ãτ+ä=0ᔆU☢■Ḅ`®VᔣW஻=X],y,zJ,ᑣ{_l]Z]=-GᦑY=1,3,-6
.[n-£>E=2j+2V3z=0l1uiuI—'I|AB,“9A8=3,2,0
,U;iABj☢ᡠᡂN஺ᑣsin6=|cosீAB,Y1ì.τ1\AB\

30\139ᡠ;iABj☢BBDEᡠᡂNḄlmm.t23.ÌíPᦪᑡ{4“}ðᦪp,ñòজq+p20,a+p=0-ঝV஻eM,%,-<“³ঞ2%+“e{a,„+a+p,a,„+a+p+\],m,஻eN*•nn1
ó4⚗2,-2,0,1Ḅᦪᑡõ2ᦪᑡᔩ´÷#ᳮᵫ³P2
¥{4}ᦪᑡḄm³3
ᔲùᙠp,útùᙠPᦪᑡ{4},T஻eN*,S,,2û,´¥ùᙠÇᡠᨵ᪵Ḅp³¥ùᙠ÷#ᳮᵫ.ூ¶ᫀ௃P1
&ᦪᑡ³ᳮᵫ¸,᪆³P2
%=]
3
ᙠp=2.ூ᪆௃ூᑖ᪆௃
1
ᵫ⚪ὃḄᓽᦪᑡᦪᑡ2
ᵫ⚪✌ᐜᦪᑡḄ4⚗ᯠ"#$%&ᓽ'Ḅ3
᪀⌼ᦪᑡ2=4+P᧕+ᦪᑡ{2}4Ḅ,ᔠ2
.Ḅ,$/01ᓽ23⚪Ḅ4ᦪPḄ.ூ6௃
1
ᵫឋ8ঞ,ᔠ⚪+0=/e{q+4+2,4+a+2+1}={2,3},2:;ᦑ4⚗2,-2,0,1Ḅᦪᑡ=&ᦪᑡ.ফឋ8জ4>0,«=0,2ᵫឋ8ঞ%+2e{a,,,a,“+l},B4=4ᡈ4=4+14=஺ᡈ4=1FG=஺ᵫឋ8ঝ+4<4ᓽ“<0ᡈ4+1<0,:;Fq=14=4+1ᵫ4<4ᨵ4+1<1:;•

31BM=4=1,஻3=4,OBP஺4=4+஺3ᡈ஻4=%+஺3+1ᡠS4=ᡈq=0.Fq=ᑣa2=4+iU{4+4+0,4+4+0+1}={2a,2a+1}={1,2},}]234=0,WX.Yq=0,ᑣ{4}Z⚗P:0,0,0,1,[☢ᵨ^_`a4"+i=஻஺=12,3),஺4"+4=஻+l(஻eN)cY஻=()efgah⚪ᡂjᎷlY஻ீn(420)eh⚪ᡂjY஻=o+1ecFi=1,ᑣpᓺr=a=%+(4&+5.sᑭᵨឋ8ঞc4k+5+a_j\jeN*,l

32S”)=41=4x2+3=2-p2°,S-S=-a=-a=-(2-/?)>0,9l0l04x2+2Bp=2,eq,%,…4o<()P20(/211)23⚪.