2023高二·全国·专题练习
解题方法
1 . 向量数量积的性质
设
都是非零向量,
是与
方向相同的单位向量,
是
与
的夹角,则:
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de036bea844c72f426254d91b6c14c98.png)
_____ ;(2)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68d5b4c0999a3a66ef0c49086c402599.png)
_____ ;(3)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba3c6bd21d9c27a68b970f446f04d6df.png)
_____ ;(4)
.
设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e8b95a61af300412fc65f846089028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c984376f5475184e0d3e4f7e1bb65f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de036bea844c72f426254d91b6c14c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68d5b4c0999a3a66ef0c49086c402599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba3c6bd21d9c27a68b970f446f04d6df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7910c1188483bdcdd3bec00c5ab4ea04.png)
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2 . (1)若
与
都是单位向量,则
.( )
(2)平面内的任意两个向量都可以作为一组基底.( )
(3)平行向量的方向一定相同.( )
(4)若
,则
或
.( )
(5)若
的面积
,则
或
.( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/778542d99ab19e2ecc0c7ef75161f133.png)
(2)平面内的任意两个向量都可以作为一组基底.
(3)平行向量的方向一定相同.
(4)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2cc1f1ef9ad32eef62aefa4c3fc3d6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d065bd10f7ea1f05764e28f095f244f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aed3d85ea66827c00b5f7e4c5ae598a.png)
(5)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a72d02ca51ae5759ee8e5ca23d3ff0e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a6794a460487525552efedd7edc4df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd4c5016bd1fc6582078299b9cf8b392.png)
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解题方法
3 . 下列结论正确的是( )
A.已知向量![]() ![]() ![]() ![]() |
B.已知单位向量![]() ![]() ![]() ![]() ![]() |
C.已知i为虚数单位,若![]() ![]() ![]() |
D.已知![]() ![]() ![]() |
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