所属成套资源:新高考数学一轮复习考点过关练习 (含解析)
新高考数学一轮复习考点过关练习 求平面向量的夹角(含解析)
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这是一份新高考数学一轮复习考点过关练习 求平面向量的夹角(含解析),共28页。
求两向量a,b的夹角θ,通常采用公式csθ=eq \f(a·b,|a||b|)进行求解.
【典例分析】
典例1.已知向量 SKIPIF 1 < 0 , SKIPIF 1 < 0 满足 SKIPIF 1 < 0 , SKIPIF 1 < 0 , SKIPIF 1 < 0 ,则 SKIPIF 1 < 0 ( )
A. SKIPIF 1 < 0 B. SKIPIF 1 < 0 C. SKIPIF 1 < 0 D. SKIPIF 1 < 0
典例2.已知平面向量 SKIPIF 1 < 0 ,则 SKIPIF 1 < 0 与 SKIPIF 1 < 0 的夹角为( )
A. SKIPIF 1 < 0 B. SKIPIF 1 < 0 C. SKIPIF 1 < 0 D. SKIPIF 1 < 0
典例3.如果平面向量 SKIPIF 1 < 0 , SKIPIF 1 < 0 .那么下列结论中正确的是( )
A. SKIPIF 1 < 0 B. SKIPIF 1 < 0
C. SKIPIF 1 < 0 与 SKIPIF 1 < 0 的夹角为 SKIPIF 1 < 0 D. SKIPIF 1 < 0 在 SKIPIF 1 < 0 上的投影向量的模为 SKIPIF 1 < 0
典例4.已知 SKIPIF 1 < 0 , SKIPIF 1 < 0 ,则下列结论中正确的个数为( )
①与 SKIPIF 1 < 0 同向共线的单位向量是 SKIPIF 1 < 0
② SKIPIF 1 < 0 与 SKIPIF 1 < 0 的夹角余弦值为 SKIPIF 1 < 0
③向量 SKIPIF 1 < 0 在向量 SKIPIF 1 < 0 上的投影向量为 SKIPIF 1 < 0
④ SKIPIF 1 < 0
A. SKIPIF 1 < 0 个B. SKIPIF 1 < 0 个C. SKIPIF 1 < 0 个D. SKIPIF 1 < 0 个
典例5.已知向量 SKIPIF 1 < 0 ,则下列说法不正确的是( )
A.若 SKIPIF 1 < 0 ,则 SKIPIF 1 < 0 的值为 SKIPIF 1 < 0 B.若 SKIPIF 1 < 0 ,则 SKIPIF 1 < 0 的值为2
C. SKIPIF 1 < 0 的最小值为1D.若 SKIPIF 1 < 0 与 SKIPIF 1 < 0 的夹角为钝角,则 SKIPIF 1 < 0 的取值范围是 SKIPIF 1 < 0
【双基达标】
6.已知向量 SKIPIF 1 < 0 , SKIPIF 1 < 0 ,则下列结论正确的是( )
A. SKIPIF 1 < 0 , SKIPIF 1 < 0 B. SKIPIF 1 < 0 ,使得 SKIPIF 1 < 0
C. SKIPIF 1 < 0 , SKIPIF 1 < 0 与 SKIPIF 1 < 0 的夹角小于 SKIPIF 1 < 0 D. SKIPIF 1 < 0 ,使得 SKIPIF 1 < 0
7.已知向量 SKIPIF 1 < 0 , SKIPIF 1 < 0 ,则 SKIPIF 1 < 0 与 SKIPIF 1 < 0 的夹角为()
A. SKIPIF 1 < 0 B. SKIPIF 1 < 0 C. SKIPIF 1 < 0 D. SKIPIF 1 < 0
8.定义空间两个向量的一种运算 SKIPIF 1 < 0 ,则关于空间向量上述运算的以下结论中恒成立的有( )
A. SKIPIF 1 < 0
B. SKIPIF 1 < 0
C. SKIPIF 1 < 0
D.若 SKIPIF 1 < 0 , SKIPIF 1 < 0 ,则 SKIPIF 1 < 0
9.设 SKIPIF 1 < 0 为实数,已知向量 SKIPIF 1 < 0 =(-1,2), SKIPIF 1 < 0 =(1, SKIPIF 1 < 0 ).若 SKIPIF 1 < 0 ,则向量 SKIPIF 1 < 0 +2 SKIPIF 1 < 0 与 SKIPIF 1 < 0 之间的夹角为( )
A. SKIPIF 1 < 0 B. SKIPIF 1 < 0 C. SKIPIF 1 < 0 D. SKIPIF 1 < 0
10.已知非零向量 SKIPIF 1 < 0 满足 SKIPIF 1 < 0 ,且 SKIPIF 1 < 0 ,则 SKIPIF 1 < 0 与 SKIPIF 1 < 0 的夹角为
A. SKIPIF 1 < 0 B. SKIPIF 1 < 0 C. SKIPIF 1 < 0 D. SKIPIF 1 < 0
11.已知向量 SKIPIF 1 < 0 , SKIPIF 1 < 0 , SKIPIF 1 < 0 ,则 SKIPIF 1 < 0 与 SKIPIF 1 < 0 的夹角为( )
A. SKIPIF 1 < 0 B. SKIPIF 1 < 0 C. SKIPIF 1 < 0 D. SKIPIF 1 < 0
12.已知向量 SKIPIF 1 < 0 ,向量 SKIPIF 1 < 0 ,则 SKIPIF 1 < 0 与 SKIPIF 1 < 0 的夹角大小为( )
A.30°B.60°C.120°D.150°
13.已知向量 SKIPIF 1 < 0 , SKIPIF 1 < 0 满足 SKIPIF 1 < 0 , SKIPIF 1 < 0 ,且 SKIPIF 1 < 0 ,则 SKIPIF 1 < 0 与 SKIPIF 1 < 0 的夹角为( )
A.30°B.60°C.120°D.150°
14.已知向量 SKIPIF 1 < 0 , SKIPIF 1 < 0 满足 SKIPIF 1 < 0 , SKIPIF 1 < 0 , SKIPIF 1 < 0 ,则 SKIPIF 1 < 0 ( )
A. SKIPIF 1 < 0 B. SKIPIF 1 < 0 C. SKIPIF 1 < 0 D. SKIPIF 1 < 0
15. SKIPIF 1 < 0 中,若 SKIPIF 1 < 0 , SKIPIF 1 < 0 ,点 SKIPIF 1 < 0 满足 SKIPIF 1 < 0 ,直线 SKIPIF 1 < 0 与直线 SKIPIF 1 < 0 相交于点 SKIPIF 1 < 0 ,则 SKIPIF 1 < 0 ( )
A. SKIPIF 1 < 0 B. SKIPIF 1 < 0 C. SKIPIF 1 < 0 D. SKIPIF 1 < 0
16.已知 SKIPIF 1 < 0 , SKIPIF 1 < 0 , SKIPIF 1 < 0 ,则 SKIPIF 1 < 0 ( )
A. SKIPIF 1 < 0 B. SKIPIF 1 < 0 C. SKIPIF 1 < 0 D. SKIPIF 1 < 0
17.已知 SKIPIF 1 < 0 、 SKIPIF 1 < 0 是圆 SKIPIF 1 < 0 上两个不同的点,且满足 SKIPIF 1 < 0 ,则 SKIPIF 1 < 0 的最大值为( )
A. SKIPIF 1 < 0 B. SKIPIF 1 < 0 C. SKIPIF 1 < 0 D. SKIPIF 1 < 0
18.已知向量 SKIPIF 1 < 0 , SKIPIF 1 < 0 , SKIPIF 1 < 0 ,满足 SKIPIF 1 < 0 SKIPIF 1 < 0 , SKIPIF 1 < 0 , SKIPIF 1 < 0 , SKIPIF 1 < 0 ,则 SKIPIF 1 < 0 与 SKIPIF 1 < 0 的夹角为( )
A. SKIPIF 1 < 0 B. SKIPIF 1 < 0
C. SKIPIF 1 < 0 D. SKIPIF 1 < 0
19.已知单位向量 SKIPIF 1 < 0 的夹角为 SKIPIF 1 < 0 ,则 SKIPIF 1 < 0 与 SKIPIF 1 < 0 夹角的余弦值为( )
A. SKIPIF 1 < 0 B. SKIPIF 1 < 0 C. SKIPIF 1 < 0 D. SKIPIF 1 < 0
20.平面向量 SKIPIF 1 < 0 , SKIPIF 1 < 0 , SKIPIF 1 < 0 ,则向量 SKIPIF 1 < 0 夹角的余弦值为( )
A. SKIPIF 1 < 0 B. SKIPIF 1 < 0 C. SKIPIF 1 < 0 D. SKIPIF 1 < 0
21.已知向量 SKIPIF 1 < 0 , SKIPIF 1 < 0 , SKIPIF 1 < 0 ,则 SKIPIF 1 < 0 与 SKIPIF 1 < 0 的夹角为( )
A. SKIPIF 1 < 0 B. SKIPIF 1 < 0 C. SKIPIF 1 < 0 D. SKIPIF 1 < 0
22.在平行四边形 SKIPIF 1 < 0 中, SKIPIF 1 < 0 ,M是 SKIPIF 1 < 0 中点.若 SKIPIF 1 < 0 ,则 SKIPIF 1 < 0 ( )
A. SKIPIF 1 < 0 B. SKIPIF 1 < 0 C. SKIPIF 1 < 0 D. SKIPIF 1 < 0
23.已知平面向量 SKIPIF 1 < 0 , SKIPIF 1 < 0 满足 SKIPIF 1 < 0 , SKIPIF 1 < 0 ,点D满足 SKIPIF 1 < 0 ,E为 SKIPIF 1 < 0 的外心,则 SKIPIF 1 < 0 的值为( )
A. SKIPIF 1 < 0 B. SKIPIF 1 < 0 C. SKIPIF 1 < 0 D. SKIPIF 1 < 0
24.设 SKIPIF 1 < 0 为单位向量,满足 SKIPIF 1 < 0 ,设 SKIPIF 1 < 0 的夹角为 SKIPIF 1 < 0 ,则 SKIPIF 1 < 0 的可能取值为( )
A. SKIPIF 1 < 0 B. SKIPIF 1 < 0 C. SKIPIF 1 < 0 D. SKIPIF 1 < 0
25.已知平面向量 SKIPIF 1 < 0 , SKIPIF 1 < 0 ,若 SKIPIF 1 < 0 ,则 SKIPIF 1 < 0 与 SKIPIF 1 < 0 的夹角为( )
A. SKIPIF 1 < 0 B. SKIPIF 1 < 0 C. SKIPIF 1 < 0 D. SKIPIF 1 < 0
【高分突破】
单选题
26.若向量 SKIPIF 1 < 0 =(1,2,0), SKIPIF 1 < 0 =(-2,0,1),则( )
A.cs〈 SKIPIF 1 < 0 〉= SKIPIF 1 < 0 B. SKIPIF 1 < 0
C. SKIPIF 1 < 0 D. SKIPIF 1 < 0
27.已知平面向量 SKIPIF 1 < 0 ,若 SKIPIF 1 < 0 ,则 SKIPIF 1 < 0 与 SKIPIF 1 < 0 的夹角的余弦值为( )
A. SKIPIF 1 < 0 B. SKIPIF 1 < 0 C. SKIPIF 1 < 0 D. SKIPIF 1 < 0
28.已知向量 SKIPIF 1 < 0 , SKIPIF 1 < 0 ,则 SKIPIF 1 < 0 面积的最大值为( )
A. SKIPIF 1 < 0 B. SKIPIF 1 < 0 C. SKIPIF 1 < 0 D.1
二、多选题
29.设向量 SKIPIF 1 < 0 ,则下列叙述错误的是( )
A. SKIPIF 1 < 0 的最小值为 2
B.若 SKIPIF 1 < 0 与 SKIPIF 1 < 0 的夹角为钝角,则 SKIPIF 1 < 0 且 SKIPIF 1 < 0
C.与 SKIPIF 1 < 0 共线的单位向量只有一个为 SKIPIF 1 < 0
D.若 SKIPIF 1 < 0 ,则 SKIPIF 1 < 0 或 SKIPIF 1 < 0
30.设向量 SKIPIF 1 < 0 =(k,2), SKIPIF 1 < 0 =(1,-1),则下列叙述错误的是( )
A.若k
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