平面向量基本定理作业

1、PAGE 平面向量基本定理作业1 设向量m2a3b，n4a2b，p3a2b，若用m，n表示p，则p_.2 在ABC中，eq o(AB,sup6()c，eq o(AC,sup6()b.若点D满足eq o(BD,sup6()2eq o(DC,sup6()，则eq o(AD,sup6()_.3. 如图，在平行四边形ABCD中，E和F分别是边CD和BC的中点，若eq o(AC,sup6()eq o(AE,sup6()eq o(AF,sup6()，其中、R，则_.4. 如图，在ABCD中，eq o(AB,sup6()a，eq o(AD,sup6()b，E、F分别是AB、BC的中点，G点使eq o(DG,

2、sup6()eq f(1,3)eq o(DC,sup6()，试以a，b为基底表示向量eq o(AF,sup6()与eq o(EG,sup6().5 如图，OACB中，eq o(OA,sup6()a，eq o(OB,sup6()b，BDeq f(1,3)BC，OD与BA相交于E.求证：BEeq f(1,4)BA. 6. 如图所示，在ABC中，点M是BC的中点，点N在边AC上，且AN2NC，AM与BN相交于点P，求证：APPM41.7. 如图，ABC中，AD为三角形BC边上的中线且AE2EC，BE交AD于G，求eq f(AG,GD)及eq f(BG,GE)的值 高一数学A-76答案1.eq f(7

3、,4)meq f(13,8)n2.eq f(2,3)beq f(1,3)c 3.eq f(4,3)4.eq o(AF,sup6()aeq f(1,2)b，eq o(EG,sup6()eq f(1,6)ab5证明设eq o(BE,sup6()eq o(BA,sup6().则eq o(OE,sup6()eq o(OB,sup6()eq o(BE,sup6()eq o(OB,sup6()eq o(BA,sup6()eq o(OB,sup6()(eq o(OA,sup6()eq o(OB,sup6()eq o(OA,sup6()(1)eq o(OB,sup6()a(1)b.eq o(OD,sup6()

4、eq o(OB,sup6()eq o(BD,sup6()eq f(1,3)ab.O、E、D三点共线，eq o(OE,sup6()与eq o(OD,sup6()共线，eq f(,f(1,3)eq f(1,1)，eq f(1,4).即BEeq f(1,4)BA.6证明设eq o(AB,sup6()b，eq o(AC,sup6()c，则eq o(AM,sup6()eq f(1,2)beq f(1,2)c，eq o(AN,sup6()eq f(2,3)eq o(AC,sup6()，eq o(BN,sup6()eq o(BA,sup6()eq o(AN,sup6()eq f(2,3)cb.eq o(AP

5、,sup6()eq o(AM,sup6()，eq o(BP,sup6()eq o(BN,sup6()，存在，R，使得eq o(AP,sup6()eq o(AM,sup6()， eq o(BP,sup6()eq o(BN,sup6()，又eq o(AP,sup6()eq o(PB,sup6()eq o(AB,sup6()，eq o(AM,sup6()eq o(BN,sup6()eq o(AB,sup6()，由eq blc(rc)(avs4alco1(f(1,2)bf(1,2)c)eq blc(rc)(avs4alco1(f(2,3)cb)b得eq blc(rc)(avs4alco1(f(1,2)

6、beq blc(rc)(avs4alco1(f(1,2)f(2,3)cb.又b与c不共线eq blcrc (avs4alco1(f(1,2)1，,f(1,2)f(2,3)0.)解得eq blcrc (avs4alco1(f(4,5)，,f(3,5).)故eq o(AP,sup6()eq f(4,5)eq o(AM,sup6()，即APPM41.7解设eq f(AG,GD)，eq f(BG,GE).eq o(BD,sup6()eq o(DC,sup6()，即eq o(AD,sup6()eq o(AB,sup6()eq o(AC,sup6()eq o(AD,sup6()，eq o(AD,sup6(

7、)eq f(1,2)(eq o(AB,sup6()eq o(AC,sup6()又eq o(AG,sup6()eq o(GD,sup6()(eq o(AD,sup6()eq o(AG,sup6()，eq o(AG,sup6()eq f(,1)eq o(AD,sup6()eq f(,21)eq o(AB,sup6()eq f(,21)eq o(AC,sup6().又eq o(BG,sup6()eq o(GE,sup6()，即eq o(AG,sup6()eq o(AB,sup6()(eq o(AE,sup6()eq o(AG,sup6()，(1)eq o(AG,sup6()eq o(AB,sup6()eq o(AE,sup6()，eq o(AG,sup6()eq f(1,1)eq o(AB,sup6()eq f(,1)eq o(AE,sup6().又eq o(AE,sup6()eq f(2,3)eq o(AC,sup6()，eq o(AG,sup6()eq f(1,1)eq o(AB,sup6()eq f(2,31)eq o(AC,sup6().eq o(AB,sup6()，eq o(AC,sup6()不