高考数学真题专项训练题集(向量)

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ᦻᦪ7.F1[2O11•ᔁ]᝞12,4BCDE/++=()ODEBA1-2A.0B.BEC.ADD.CFᜧ
ᦻᦪ7.F1[2O11.ᔁ]Dூ᪆௃BA+CD+EF=BA+AF-BC=BF-BC=&,ᡠ⌱D.ᜧ
ᳮᦪ4.F1ODEBA1T[2011.ᔁ]᝞11,ABCZ5EFBA+CD+EF=()A.0B.BEC.ADD.CFᜧ
ᳮᦪ4.F1[2O11.ᔁ]Dூ᪆௃BA+CD+EF=BA+AF-BC=BF-BC=&,ᡠ⌱D.

1᪗ᳮᦪ1O.F22O11.ᓅᔁ!"#ᔣ%஺=()1),*=(0,-1),c=(k,)).a2b,cᐳ.ᑣ0=.᪗ᳮᦪ1O.F22O11.ᓅᔁ!1ூ᪆௃12a—26=()3),ᵫa-24,cᐳ.ᨵ^^=7^89:=1.᪗ᦻᦪH.F22011•ᓅᔁ!<#ᔣ%a=()1),6=(0,—1),c={k,᝞=@2஺,cᐳ.ᑣ?=᪗ᦻᦪU.F22011•ᓅᔁ!1ூ᪆௃12a—2஺=(3),ᵫa—24,cᐳ.ᨵ@=>89:=1.᪗ᦻᦪ3.F22011•BCᔁ!"#ᔣ%a=(l,2),b=(l,0),c=(3,4).=*2Dᦪ(a+Xb)//c,Elj2=()A.FB.FC.1D.2᪗ᦻᦪ3.F22011•BCᔁ!Bூ᪆௃12a+G=(1,2)+2(!,0)=(1+2,2),H12(°+K)஻c,ᡠ(l+»X4-2><3=0,94=/᪗ᦻᦪ13.F22011Mᓭᔁ!Oᔣ%a,PQRভ=2)b=(2,I),T஺,bḄ4ᔣVWᑣaḄᙶ᪗2.᪗ᦻᦪ13.F22011Mᓭᔁ!(4,-2)ூ᪆௃12a,*Ḅ4ᔣVW᪷Zᐳ.ᔣ%[\ᨵ]஺=^%<0),ᡠa=(2a2).ᵫb=2)(24)2+/=2)=c=—2ᡈ4=2(fg),ᦑ•=(-4,—2).᪗ᳮᦪ12.F2Q011•kCᔁ!O4,A2,A3,lm☢opᙶ᪗qrrsbḄt=t3=u»(4w□t4=஻ᡧ2a6zT++{=2,ᑣ|A34}~ᑖᒘA,A2,"#m☢ḄtC,஺}~ᑖᒘt4,B,ᑣ☢Ḅl()A.C8l.ABḄtB.஺8l.ABḄtC.Cஹ஺8bᙠ.ABD.Cஹ஺s8bᙠ.ABḄ.᪗ᳮᦪ12.F22011•kCᔁ!Dூ᪆௃=Cஹ஺}~ᑖᒘtAFB,ᑣn=2(46ff1IR),AD—fiAB(/i^R),T—=2.■ZlfJA]=Cl.A8Ḅtᑣ==2=3=஺=0,ᦑA⌱⚗┯FbᳮB⌱⚗┯;

2C]=CஹAbᙠ.ABᑣ0<2<1,0<“<1:+9>2,C⌱⚗┯FD]=Cஹ஺bᙠ.A8Ḅ.ᑣ7>1,"Alnq+B஺ᦑCஹ஺s8bᙠ.ABḄ.D⌱⚗.᪗ᦻᦪ12.F2I2011•kCᔁ!O4,A2,A3,4lm☢opᙶ᪗qrrsbḄt=4«3="12(4c1t)4®4=஻4¯2஺/610T■+{=2,ᑣ|A34}~ᑖᒘA1Ai,"#tC(c,0),D(d,0)(c,4WR)}~ᑖᒘtA(0,0),B(l,0),ᑣ☢Ḅl()A.C8l.ABḄtB.஺8l.A8ḄtC.Cஹ஺8bᙠ.ABD.Cஹ஺s8bᙠ.ABḄ.᪗ᦻᦪµ2.F2µ2011.kCᔁ!Dூ᪆௃ᵫ¶[\#·=¸ᓽ(c,0)="1,0),.,.4=c.bᳮA£>=஻»ᓽ("0)=஻(1,0),.•.஻=¼,H--+ᓝ=2,.•.]+*=2.=tC2.A8tᑣ]=2,,4+4=2¾¿ᡠCs2.ABtbᳮ஺s2.A8AA/Zt.C,஺bᙠ.ABEᕷ+ஹ2,.♦.ÂÃtᙠ.ABÄÃtᙠ.ABḄ..᪗ᳮᦪ14.F2I2011•ᜩÆᔁ!"#opÇABC஺AD//BC,ZADC=90°,AD=2,BC=\,ÈlῪQCḄGtElj|Í+3r|Ḅᨬ)Ï2.᪗ᳮᦪ14.F2µ2011•ᜩÆᔁ!5ூ᪆௃ÑÒ᝞1—6ᡠÓḄᙶ᪗qO஺C=஻ᑣA(2,0),8(1,h).OÈ(0,y),(0WyW஻)ᑣÕ=(2,~y),PB=(\,h-y),|Ö+3Í|=k5+(3஻-4»)22×=5.᪗ᦻᦪ14.F2µ2011•ᜩÆᔁ!"#opÇABC஺AD//BC,ZADC=90°,AO=2,BC=\,PlῪOCḄGtᑣ|Ú+3r|Ḅᨬ)Ï2.

3᪗ᦻᦪ14.F2µ20U.ᜩÆᔁ!5ூ᪆௃ÑÒ᝞1—6ᡠÓḄᙶ᪗qO£>C=஻ᑣ4(2,0),8(1,/?).OP(0,y),(OWyW/2)ᑣÍ=(2,—y),PB=(\,h~y),Ý|Þ+3|=^25+(3஻-4y)22ß=5.᪗ᳮᦪ14.F2µ20U•àáᔁ!=m☢ᔣ%᝞âQRভ=1,WIW1,Tᔣ%ᜐ᜛2åḄmæḄ☢ç2ᑣa,᜛Ḅᜳp0ḄêÏìl.n5n᪗ᳮᦪ14.F2µ2011•àáᔁ!6_,T_VIa1=1,ôWl,F.sin஺=^^ூ᪆௃ᵫ⚪ï9:|a||P|sin9n5nHn),*.9es᪗ᦻᦪ15.F2µ2011•àáᔁ!=m☢ᔣ%a,/?QRಘ=1,”|W1,Tᔣ%a,“2÷BḄmæḄ☢ç2ᩈᑣa~6Ḅᜳp6ḄêÏìl.ூ᪆௃ᵫ⚪ï9|a|W|sin8=b=1,᪗ᦻᦪ15.F2Q011•àáᔁ!ù1,F.sin஺=úûH"6(0,“)*.0G

4᪗ᦻᦪ14.F3[2011•ýþᔁ]
ᔣ0,(a+2b>(a-Z»)=-6,=1,\b\=2,ᑣ஺bḄᜳ.!᪗ᦻᦪ14.F3[2011•*+ᔁ]ூ/ᫀ௃yூ3᪆௃5஺6Ḅᜳ78⚪:ᨵ(a+2b>(a—஻)=/+“6—2"=-7+2cos஺=1,JI—6,ᡠFcos஻=].Gn,ᦑ6=J.!᪗ᳮᦪ13.F3[2011•*+ᔁ]
ᔣa,L(a+2b>(a—b)=—6,M=1,ᳮ=2,ᑣ஺6Ḅᜳ.!᪗ᳮᦪ13.F3[2011•*+ᔁ]yூ3᪆௃5஺NḄᜳ0,8⚪:ᨵ(a+26>(aCC131஺)=0~+0•6-2Zr=—7+2cos᜛=—6,ᡠFcos᜛=/.G0W8+4i=3,ᑣ\a+2b\=y/3,ᦑ⌱B.!᪗ᳮᦪ8.E5,F3[2011•lmᔁ]
஺nᙶ᪗pq^qA(—l,1),sqM(x,y)uX+y22,☢xyzḄ{|q^ᑣ}1•⊈Ḅn()ஹ)W2A.[-1,0]B.[0,1]C.[0,2]D.[-1,2]!᪗ᳮᦪ8.E5,F3[2011•lmᔁ]Cூ3᪆௃⊤Ḅu☢xy(᝞12),5X•=-x+y,᪗ᦪz=—x+y,ᓽ+z,᳛1Ḅu^qC(l,1)^Zᨵᨬ^ᓽZmin=-1+1=0]qB(0,2)^Zᨵᨬᜧ^ᓽZmax=-0+2=2.ZḄn[0,21^ᓽ᧊•¤Ḅn[0,2],ᦑ⌱C.

5!᪗ᦻᦪ13.F32011•lmᔁ¥sᔣ0=(1,1),*=(-1,2),ᑣa¦§.!᪗ᦻᦪ13.F32011•lmᔁ¥1ூ3᪆௃ᵫ©
a=(l,1),b=(T,2),ªa4=lX(-1)+1X2=1.!᪗ᳮᦪ3.F32011•«¬ᔁ¥sᔣa,b,ca"a_Zc,ᑣc-(a+2b)=()A.4B.3C.2D.0!᪗ᳮᦪ3.F32011•«¬ᔁ¥Dூ3᪆௃Ga%a®c,ᡠFᡠFc-(a+2b)=c-a+2b-c—0.!᪗ᦻᦪ2.F3[2011¯ᓅᔁ]sᔣa=(l,2),Z>=(1,-1),ᑣ2a+Z>Q—6Ḅᜳ§()jinn3±A.-yB.yC.yD,—!᪗ᦻᦪ2.F3[2011•¯ᓅᔁ]Cூ3᪆௃G2a+b=(2,4)+(1,-1)=(3,3),a—b=(0^3),ᡠF|2a+Z>|=36^|a—6|=3.52a+ba-bḄᜳ7ᑣcos^=(2a+b)(a—b)(3,3).(0,3)/rnee[0,31].ᡠF஺=².|2a+b||a—“36032!᪗ᳮᦪ14.F32011•¯ᓭᔁ¥ᙠµ¶1Ḅ·¸¹ABCº^5»=2^CA=3CE,ᑣ•BE=.!᪗ᳮᦪ14.F312011.¯ᓭᔁ¥(ூ3᪆௃ᵫ⚪
^஺8cºq^£CE¸ᑖq,FBCᡠᙠḄ¾x¿^F4஺ᡠᙠḄ¾y¿^mÀu☢¾ᙶ᪗Á^ªA(0,ᙶ),£)(0,0),B(—0),EQ,Ã)^ᦑÄ=(0,—ᙶ)^Å=Æ^)^ᡠF•ᓰ⁠Xᙶ=-1.204!᪗ᳮᦪ1LF3Q011•ÉÊᔁ¥
M=|Ë=2,(a+2i)«(a-&)=-2,ᑣ஺ÌḄᜳ!᪗ᳮᦪH.F32011•ÉÊᔁ¥ூ/ᫀ௃yூ3᪆௃5@ÌḄᜳ7ᵫ(a+2»(஺-b)=—2ª|a|2+a-*-2|*|2=4+2X2Xcos஺-2X4=-2,1n3ªcos0=-,9=-^.!᪗ᦻᦪU.F32011•ÉÊᔁ¥
Î{ᓫÐᔣ^&ḄᜳÒ"^sᔣᔊ=Ô2&^Õ=3ei+4/^ᑣ61•Ö=

6!᪗ᦻᦪll.F3[2011•ÉÊᔁ]6ூ3᪆௃ᵫ⚪5
M=▢|=1d•&=5^ᡠFb\•Õ=®-2&>(3஺1+4«2)=3Ù2Ú•8⍩=3—2X]—8=-6.!᪗ᳮᦪ10.F3[2011.!᪗ᐰYᔁ]
஺஻ᙳᓫÐᔣ^ᐸᜳ7ᨵÞᑡà{á⚪âPi*|஺+)|>1=஺ᵯ,ᑴ;஻2â|a+6|>1=æ,P3*|஺Ì|>1=஺ᵯ,y)P4*I஺çË>1=஺£(è,nᐸºḄéá⚪n()A.P1^஻4B.0,P3C.P2,"3D.஻2^஻422!᪗ᳮᦪ10.F3[2011•!᪗ᐰYᔁ]Aூ3᪆௃Gê+ᜐ>1=+2a-b+\b\>\<^ab>_1~20|a||஻cos£=cos஺>]ì᜛e[o,W^ᡠFíéá⚪^P2Ꮇá⚪.G|஺">1=M—2a-b+\b\>l=a0<^=|஻||"cos®=cos᜛ᐔ^ᡠFP4éá⚪^P3Ꮇá⚪.!᪗ᳮᦪ10.F3[2011•ðñᔁ]sa,b,஺ᙳᓫÐᔣ^஻6=0,(a—c)S-c)W&,ᑣ|a+b—c|Ḅᨬᜧ()A.V2-1B.1C.&D.2!᪗ᳮᦪ10.F3[2011•ðñᔁ]Bூ3᪆௃\a+b-c\=yj(a+b—c)2=,^a2+Z>2+c2+2aZ>—2ac—ᵫ§Q•6=0,ᡠFz=^3—2c(a+Ì),ᵫ§(a—c)•()—c)W0,ª(a+b>c2c2=i,ᡠF|஻+஻஺|=^3—2஺(a+6)Wl,ᦑ⌱B.!᪗ᦻᦪ3.F3[2011•ðñᔁ]
ᔣa=(21),6=(—1,A),a-(2a-b)=0òijk=()ffA.-12B.-6C.6D.12!᪗ᦻᦪ3.F3[20U•ðñᔁ]Dூ3᪆௃a\2a-b)=2a2-ab=0ᓽ10—(ᦇ-2)=0,fᡠFᦇ=12,ᦑ⌱D.!᪗ᦻᦪ13.F3[2011•!᪗ᐰYᔁ]
஺bÎ{ᐳḄᓫÐᔣ^k23ᦪ,sᔣa+bᔣka-bᚖ¾^ᑣk=.2!᪗ᦻᦪ13.F3[2011•!᪗ᐰYᔁ]1ூ3᪆௃ᵫ⚪:^ª(a+b)•(ö6)=ᵨ஺|~ab+

7kab~\b\=%+(4—l)a-஻1=(A—1)(1+a/)=0,Ga஺ᐳ^ᡠFa?#—1,ᡠFø—1=0,3ª&=1.!᪗ᳮᦪ18.F3,C8[2011•▷Êᔁ]úûü»ýþÿᳮ.᪗ᳮᦪ18.F3,C8[2011•▷ᔁ]ூ௃ᳮḄᐸḄ!"#$ᜳḄ&'Ḅ(.ᡈᙠ+A8C,-a,b,c2A,B,CḄ.-ᨵ4="+c2—2bccosA,h2=c1+a2-2cacosB,c2=cr+b2-2abcosC.01᝞319,319a2=BC•BC=(.AC-AB)(AC-AB)=M*2-2AC-AB+AB2=AC2-2\AC\•|AB|cosA+Afi2=b2—2bccosA+c2,ᓽa1=b1+c1—2hccosA.5ᳮ60b2=c2+ci1—2cacosB,c2=a2+b2-2ahcosC.01789AABC,-4,B,஺ᡠ.ᑖ=>?b,c,@A>AB-ABᡠᙠCD>xEFGCᙶ᪗I(᝞31—10)-31-10ᑣC(bcosAbsinA)B(c,0),tta2=\BC\2=(Z?cosA-c)2+(fesinA)2=62cos2A_2bccosA+c2+Z?2sin2A=b2+c1-2hccosA.5ᳮ60b1=c2+O1-2cacosB,c1=a1+h1-2ahcosC.

8᪗ᦻᦪ18.F3,C8[2011•▷ᔁ]OPQ0Rᳮ.᪗ᦻᦪ18.F3,C8I20U.▷ᔁேூ௃ᳮḄᐸḄ!"#$ᜳḄ&'Ḅ(.ᡈᙠAABC,-a,b,c>A,B,஺Ḅ.-ᨵa2=b2+c2-2bccosA,/=c2+/2cacosB,c2=a2+b2-2abcosC.01᝞31-10,a1=BC•BC=(AC-AB)\AC-AB)=AC2-2AC•AB+AB2=AC2-2|AC|•\AB\cosA+AB2=/?2—2bccosA+c2ᓽaz=b2-\-c2—2hccosA,5ᳮ60b2=c1+a2—2cacosB,c1=a1+b1-2abcosC.01789+ABC,-A,B,Cᡠ.ᑖ=>a,b,c,@A>AB-ABᡠᙠCD>xEFGCᙶ᪗I,ᑣCScosA,fesinA),B(c,0),a2=|BC]2=(bcosA—c)2+(fesinA)2=b2cos2A_2hccosA+c2+fe2sin2A=lr+c2-2bccosA.5ᳮ60h2=c2+a2—2cacosB,c2=/+஻—2abeosC.᪗ᦪW10.F3[20UXYᔁ]89ei-&[ᜳ>\Ḅ]ᓫ_ᔣa-஺=Ḅ2e?,h=kei+e2,c஺•d=0-ᑣeᦪfḄg>.᪗ᦪW1O.F3[2O1IXYᔁ]/ூ᪆௃j>aS=®-2e2)«e/+e2)=&e-+(l—2k)(ej•e2)~~2ej,

9l|ᑗ=o2|=1,ei•e=-I-ᡠ@2k—2=0,ᓽp2ᜧrᳮᦪ12.F3[2011•stᔁ]89ᓫ_ᔣaḄ,02Ḅᜳ>60°,ᑣ|2eue2|=.ᜧrᳮᦪ12.F3[2011stᔁ]#ூ
᪆]\2ei-e\2^4e]-4ei-e+ei22=4|g|2—4©|©|,cos60°+|«2/=4Xp_4X1X1x|+y=3,|2«i—C2|—A/3.ᜧrᦻᦪ5.F3[2011•stᔁ]89ᔣa஺=(1,k),b=Q,2),la+஻"aᐳD-xyaḄg>()A.1B.2C.3D.4ᜧrᦻᦪ5.F3[2011•stᔁ]Dூ
᪆௃ᵫᩩ}9a+b=(3,k+2),"QᐳD--3X%-lX(&+2)=0,~4=1,*.a•6=1X2+1X2=4.ᦑ⌱D.

10ᜧrᳮᦪ12.F4[2011•ᐰᔁ]ᔣaa,b,c5==1,aO,Bᑖ=>A,B,C,ᵫ89ᩩ}~-NAOB=120°,ZACB=60°,ᑣBCᙠ+AOSḄ᜜ᙊ-OCᙊ-|c|ᨬᜧ-ᙠAAOB,-~AB=ᩈ,ᵫᳮ~+AOB᜜ᙊḄC[.஺=2,|c|Ḅᨬᜧg[2,ᦑ⌱A.sin120