2022年平面向量部分常见的考试题型总结 .pdf
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1、_ 精品资料平面向量部分常见的题型练习类型(一):向量的夹角问题1.平面向量ba,,满足4,1ba且满足2.ba,则ba与的夹角为2.已知非零向量ba,满足)(,abbba2,则ba与的夹角为3.已知平面向量ba,满足424)2.(bababa,且)(且,则ba与的夹角为4.设非零向量a、b、c满足cbacba|,|,则ba,5.已知的夹角。与求bababa,7,3,26.若非零向量ba,满足,0).2(bbaba,则ba与的夹角为类型(二):向量共线问题1.已知平面向量),(xa32,平面向量),(182b若ab,则实数x2.设向量),(),(3212ba若向量ba与向量)74(,c共线,则
2、3.已知向量),(),(xba211若abba24与平行,则实数x的值是()A-2 B0 C1 D2 _)10,(),54(),12,(.4kCBAkOCOBkOA则三点共线,且,已知向量5已知),(),(),(73231xCBA,设aAB,bBC且ab,则 x 的值为()(A)0(B)3(C)15(D)18 6已知a=(1,2),b=(-3,2)若 ka+2b与 2a-4b共线,求实数k 的值;7已知a,c是同一平面内的两个向量,其中a=(1,2)若52c,且 a c,求c的坐标8.n 为何值时,向量),(1na与),4(nb共线且方向相同?_ 精品资料9.已知且),2,1(,3 baab,
3、求a的坐标。10.已知向量)2,1(,112cmba),(),(,若(ba)c,则 m=11.已知ba,不共线,badbakc,,如果cd,那么k=,c与d的方向关系是12.已知向量且),(),(,221mbaab,则ba32类型(三):向量的垂直问题1已知向量babxa且),()6,3(,1,则实数x的值为2已知向量abbanbna垂直,则与),若,(),(2113已知a=(1,2),b=(-3,2)若 ka+2b与 2a-4b垂直,求实数k 的值4已知4,2 ba,且ba与的夹角为3,若的值垂直,求与kbakbak22。5.已知),1,1(),0,1(ba求当为何值时,aba与垂直?6.已
4、知单位向量mmnnm),求证:(的夹角为和237.已知,24),(a求与a垂直的单位向量的坐标。8.已知向量的值为垂直,则实数与且向量),(bababa2)0,1(,239.kbcakcba,则)若(,),(),2,()3,1(,1310.)满足于(,若向量),(accba)3,2(,21b,_cbac),则(类型(四)投影问题1 已知,4,5 ba,ba与的夹角32,则向量b在向量a上的投影为2 在RtABC中,ACABACC.,4,2则3关于caba.且0a,有下列几种说法:)(cba;bc;0).(cbab在a方向上的投影等于c在a方向上的投影;ab;cb文档编码:CK6O6P7T5V3
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9、 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3
10、T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3
11、 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6_ 精品资料其中正确的个数是()(A)4 个(B)3 个(C)2 个(D)1 个类型(四)求向量的模的问题1.已知零向量bbabaa,则),(25,10.,122.已知向量ba,满足bababa,则2,2,13.已知向量a)3,1(,bab,则)0,2(4已知向量baba则),cos,1(),sin,1(的最大值为5.设点M是线段BC的中点,点A在直线BC外,()则 AMACABACABB
12、C,162(A)8(B)4(C)2(D)1 6.设向量a,b满足1ba及334ba,求ba53的值7.已知向量ba,满足,3.,5,2baba求baba和8.设向量a,b满足的值为则babaaba2),2(,2,1类型(五)平面向量基本定理的应用问题1若a=(1,1),b=(1,-1),c=(-1,-2),则c等于()(A)ba2321(B)ba2321(C)ba2123(D)ba21232.已知baccba的值,使和),求,(),(),(0111013.设ee21,是平面向量的一组基底,则当_,21时,02211ee4.下列各组向量中,可以作为基底的是()(A)2,1(),0,0(21ee(
13、B)7,5(),2,1(21ee(C)10,6(),5,3(21ee(D)43,21(),3,2(21ee文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK
14、6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S
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16、6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S
17、2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK
18、6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S
19、2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6文档编码:CK6O6P7T5V3 HA7R8X1Y9S2 ZV3T8V3T8E6_ 精品资料5.(),则,(),(),(ccba241111(A)ba3(B)ba3(C)ba3(D)ba3dcdcdcmRmbamdbacbaba求平行与若为何值时)当()(,的夹角为与已知,)2?(,1623,2,3.6类型(六)平面向量与三角函数结
20、合题1.已知向量(2sin,cos)42xxm,(cos,3)4xn,设函数()f xm n求函数()f x 的解析式(2)求()f x 的最小正周期;(3)若0 x,求()f x 的最大值和最小值2.已知322,A、B、C 在同一个平面直角坐标系中的坐标分别为(3,0)A、(0,3)B、(cos,sin)C。(I)若|ACBC,求角的值;(II)当1AC BC时,求22sinsin(2)1tan的值。3.已知ABC的三个内角A、B、C 所对的三边分别是a、b、c,平面向量)sin(,1(ABm,平面向量).1),2sin(sinACn(I)如果,3,3,2SABCCc的面积且求 a 的值;(
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