1 . 互相垂直且有公共原点的两条数轴构成平面直角坐标系.如果坐标系中两条坐标轴不垂直,那么这样的坐标系称为斜坐标系.如图,设Ox,Oy是平面内相交成60°角的两条数轴,
,
分别是与x轴、y轴正方向同向的单位向量.若向量
,则把有序数对
叫做向量在斜坐标系xOy中的坐标.
,求
;
(2)已知
,
,求
;
(3)若
,
,
与
的夹角记为
,求
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0411792b587ddd3e04440392f011c224.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b95d660852c5226ff65a21cfb36b8b39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5253a9a71037d60059b60237824193b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d9aa1d34d66a6876aa0566c8fc8b0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff1b27f67a2190739f8fe8d71ad22652.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88b14123852c3e17f0a519282e076797.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eed0a6833e003a624c53cc85c8fd902f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5d91ab16e20df003977ad6d60fd590e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/854e16eb319ee454088f5b527cf6c4d5.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e66a915e485aa05087b5368c09ed4870.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9117ab8f2d06b2dd239d29987a33977b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e163480714acc9dae5005cac65d217d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c37564ec4e9e92485f1769e8ffaac31d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
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2024-03-21更新
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3卷引用:吉林省长春市实验中学2023-2024学年高一下学期第一学程(4月)考试数学试题