配套习题- 向量运算与正、余弦定理的综合应用 -【青果学院】

1/3单选题

难度：

1.已知

ABC，向量m=(

,1-

)与n=(2,0)的夹角的余弦值为

，则角B的大小为（）

A
B
C
D

正确答案：Qw==

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

2/3单选题

难度：

2.在△ABC中，角A、B、C所对的边分别为a、b、c（其中a≤b≤c），设向量

＝(cosB，sinB)，

，且向量

为单位向量，b＝

，a＝1，则△ABC的面积为（）

A
B
C
D

正确答案：Qg==

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

3/3单选题

难度：

3.已知函数f(x)＝sinxcosx+

cos²x-

的最大值为a，最小值为b，若向量（a，b）与向量（cosθ，sinθ）垂直，则锐角θ的值为（　　）

A
B
C
D

正确答案：Qw==

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