2023屆一輪復(fù)習(xí)北師大版 平面向量的概念及線性運(yùn)算 作業(yè)

1、 課時(shí)分層作業(yè)(三十二)平面向量的概念及線性運(yùn)算 一、選擇題1如圖所示，在正六邊形ABCDEF中，eq o(BA,sup8()eq o(CD,sup8()eq o(EF,sup8()等于()A0Beq o(BE,sup8()Ceq o(AD,sup8()Deq o(CF,sup8()D由圖知，eq o(BA,sup8()eq o(CD,sup8()eq o(EF,sup8()eq o(CD,sup8()eq o(DE,sup8()eq o(EF,sup8()eq o(CF,sup8()，故選D2(2021天水月考)已知a，b是兩個(gè)非零向量，且|ab|a|b|，則下列說法正確的是()Aab0Ba

2、bCa與b共線反向D存在正實(shí)數(shù)，使abD由a，b是非零向量且|ab|a|b|知，向量a，b是方向相同的共線向量，故選D3設(shè)D，E，F(xiàn)分別為ABC的三邊BC，CA，AB的中點(diǎn)，則eq o(EB,sup8()eq o(FC,sup8()()Aeq o(AD,sup8()Beq f(1,2)eq o(AD,sup8()Ceq f(1,2)eq o(BC,sup8()Deq o(BC,sup8()A由題意得eq o(EB,sup8()eq o(FC,sup8()eq f(1,2)(eq o(AB,sup8()eq o(CB,sup8()eq f(1,2)(eq o(AC,sup8()eq o(BC,s

3、up8()eq f(1,2)(eq o(AB,sup8()eq o(AC,sup8()eq o(AD,sup8()4已知向量eq o(AB,sup8()a3b，eq o(BC,sup8()5a3b，eq o(CD,sup8()3a3b，則()AA，B，C三點(diǎn)共線BA，B，D三點(diǎn)共線CA，C，D三點(diǎn)共線DB，C，D三點(diǎn)共線Beq o(BC,sup8()eq o(CD,sup8()2a6b2(a3b)2eq o(AB,sup8()，eq o(BD,sup8()2eq o(AB,sup8()，A，B，D三點(diǎn)共線，故選B5在ABC中，eq o(AN,sup8()eq f(1,4)eq o(NC,sup

4、8()，P是直線BN上一點(diǎn)，若eq o(AP,sup8()meq o(AB,sup8()eq f(2,5)eq o(AC,sup8()，則實(shí)數(shù)m的值為()A4B1C1D4Beq o(AN,sup8()eq f(1,4)eq o(NC,sup8()，eq o(AC,sup8()5eq o(AN,sup8()又eq o(AP,sup8()meq o(AB,sup8()eq f(2,5)eq o(AC,sup8()，eq o(AP,sup8()meq o(AB,sup8()2eq o(AN,sup8()，由B，P，N三點(diǎn)共線可知，m21，m16(2021南昌模擬)如圖，在ABC中，點(diǎn)D在BC邊上，且

5、CD2DB，點(diǎn)E在AD邊上，且AD3AE，則用向量eq o(AB,sup8()，eq o(AC,sup8()表示eq o(CE,sup8()為()Aeq f(2,9)eq o(AB,sup8()eq f(8,9)eq o(AC,sup8()Beq f(2,9)eq o(AB,sup8()eq f(8,9)eq o(AC,sup8()Ceq f(2,9)eq o(AB,sup8()eq f(7,9)eq o(AC,sup8()Deq f(2,9)eq o(AB,sup8()eq f(7,9)eq o(AC,sup8()B由平面向量的三角形法則及向量共線的性質(zhì)可得eq o(CE,sup8()eq

6、o(AE,sup8()eq o(AC,sup8()eq f(1,3)eq o(AD,sup8()eq o(AC,sup8()eq f(1,3)(eq o(AB,sup8()eq f(1,3)eq o(BC,sup8()eq o(AC,sup8()eq f(1,3)eq blcrc(avs4alco1(o(AB,sup8()f(1,3)o(AC,sup8()o(AB,sup8()eq o(AC,sup8()eq f(2,9)eq o(AB,sup8()eq f(8,9)eq o(AC,sup8()7已知平面內(nèi)一點(diǎn)P及ABC，若eq o(PA,sup8()eq o(PB,sup8()eq o(PC

7、,sup8()eq o(AB,sup8()，則點(diǎn)P與ABC的位置關(guān)系是()A點(diǎn)P在線段AB上B點(diǎn)P在線段BC上C點(diǎn)P在線段AC上D點(diǎn)P在ABC外部Ceq o(PA,sup8()eq o(PB,sup8()eq o(PC,sup8()eq o(AB,sup8()eq o(AP,sup8()eq o(PB,sup8()，eq o(PC,sup8()2eq o(PA,sup8()，因此點(diǎn)P在線段AC上，故選C8設(shè)O在ABC的內(nèi)部，D為AB的中點(diǎn)，且eq o(OA,sup8()eq o(OB,sup8()2eq o(OC,sup8()0，則ABC的面積與AOC的面積的比值為()A3B4C5D6B如圖，

8、D為AB的中點(diǎn)，則eq o(OD,sup8()eq f(1,2)(eq o(OA,sup8()eq o(OB,sup8()，又eq o(OA,sup8()eq o(OB,sup8()2eq o(OC,sup8()0，eq o(OD,sup8()eq o(OC,sup8()，O為CD的中點(diǎn)，又D為AB中點(diǎn)，SAOCeq f(1,2)SADCeq f(1,4)SABC，則eq f(SABC,SAOC)4二、填空題9若|eq o(AB,sup8()|eq o(AC,sup8()|eq o(AB,sup8()eq o(AC,sup8()|2，則|eq o(AB,sup8()eq o(AC,sup8()

9、|_2eq r(3)由|eq o(AB,sup8()|eq o(AC,sup8()|eq o(AB,sup8()eq o(AC,sup8()|2知ABC是等邊三角形，設(shè)BC的中點(diǎn)為D，則|eq o(AB,sup8()eq o(AC,sup8()|2|eq o(AD,sup8()|2eq r(3)10已知向量a，b不共線，且cab，da(21)b，若c與d共線反向，則實(shí)數(shù)的值為_eq f(1,2)由于c與d共線反向，則存在實(shí)數(shù)k使ckd(k0)，于是abka(21)b整理得abka(2kk)b由于a，b不共線，所以有eq blcrc (avs4alco1(k，,2kk1，)整理得2210，解得1

10、或eq f(1,2)又因?yàn)閗0，所以0，故eq f(1,2)11在等腰梯形ABCD中， eq o(AB,sup8()2eq o(DC,sup8()，點(diǎn)E是線段BC的中點(diǎn)，若eq o(AE,sup8()eq o(AB,sup8()eq o(AD,sup8()，則_，_eq f(3,4)eq f(1,2)取AB的中點(diǎn)F，連接CF(圖略)，則由題可得CFAD，且CFADeq o(AE,sup8()eq o(AB,sup8()eq o(BE,sup8()eq o(AB,sup8()eq f(1,2)eq o(BC,sup8()eq o(AB,sup8()eq f(1,2)(eq o(FC,sup8()

11、eq o(FB,sup8()eq o(AB,sup8()eq f(1,2)eq blc(rc)(avs4alco1(o(AD,sup8()f(1,2)o(AB,sup8()eq f(3,4)eq o(AB,sup8()eq f(1,2)eq o(AD,sup8()，eq f(3,4)，eq f(1,2)12已知ABC和點(diǎn)M滿足eq o(MA,sup8()eq o(MB,sup8()eq o(MC,sup8()0，若存在實(shí)數(shù)m使得eq o(AB,sup8()eq o(AC,sup8()meq o(AM,sup8()成立，則m_3由已知條件得eq o(MB,sup8()eq o(MC,sup8()

12、eq o(MA,sup8()，M為ABC的重心，eq o(AM,sup8()eq f(1,3)(eq o(AB,sup8()eq o(AC,sup8()，即eq o(AB,sup8()eq o(AC,sup8()3eq o(AM,sup8()，則m31已知等邊三角形ABC內(nèi)接于O，D為線段OA的中點(diǎn)，則eq o(BD,sup8()()Aeq f(2,3)eq o(BA,sup8()eq f(1,6)eq o(BC,sup8()Beq f(4,3)eq o(BA,sup8()eq f(1,6)eq o(BC,sup8()Ceq o(BA,sup8()eq f(2,3)eq o(BC,sup8()

13、Deq f(2,3)eq o(BA,sup8()eq f(1,3)eq o(BC,sup8()A設(shè)BC的中點(diǎn)為E，由題意知，點(diǎn)O為等邊ABC的重心，則eq o(AD,sup8()eq f(1,3)eq o(AE,sup8()，eq o(BD,sup8()eq o(BA,sup8()eq o(AD,sup8()eq o(BA,sup8()eq f(1,3)eq o(AE,sup8()eq o(BA,sup8()eq f(1,3)(eq o(AB,sup8()eq o(BE,sup8()eq f(2,3)eq o(BA,sup8()eq f(1,6)eq o(BC,sup8()故選A2如圖，在AB

14、C中，eq o(AN,sup8()eq f(2,3)eq o(NC,sup8()，P是BN上一點(diǎn)，若eq o(AP,sup8()teq o(AB,sup8()eq f(1,3)eq o(AC,sup8()，則實(shí)數(shù)t的值為()Aeq f(2,3)Beq f(2,5)Ceq f(1,6)Deq f(3,4)C法一：因?yàn)閑q o(AN,sup8()eq f(2,3)eq o(NC,sup8()，所以eq o(AN,sup8()eq f(2,5)eq o(AC,sup8()設(shè)eq o(NP,sup8()eq o(NB,sup8()，則eq o(AP,sup8()eq o(AN,sup8()eq o(N

15、P,sup8()eq f(2,5)eq o(AC,sup8()eq o(NB,sup8()eq f(2,5)eq o(AC,sup8()(eq o(NA,sup8()eq o(AB,sup8()eq f(2,5)eq o(AC,sup8()eq blc(rc)(avs4alco1(f(2,5)o(AC,sup8()o(AB,sup8()eq o(AB,sup8()eq f(2,5)(1)eq o(AC,sup8()又eq o(AP,sup8()teq o(AB,sup8()eq f(1,3)eq o(AC,sup8()，所以teq o(AB,sup8()eq f(1,3)eq o(AC,sup8()eq o(AB,sup8()eq f(2,5)(1)eq o(AC,sup8()，得eq blcrc (avs4alco1(t，,f(2,5)1f(