1 . 在平面直角坐标系中,设向量
,
,其中
、
为
的两个内角.若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26308ea6d8f321d27acbd7f9b131f9f1.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8f5b333e5fd7d373db18589806095b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/082c9a9e7088be6ac0f41537a27995cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33ee59964f020fc52b5ba66a3f5fcc3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26308ea6d8f321d27acbd7f9b131f9f1.png)
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2 . 如图,已知
、
分别是正方形
边
、
的中点,
与
交于点
,
、
都垂直于平面
,且
,
,
是线段
上一动点.
![](https://img.xkw.com/dksih/QBM/2021/10/15/2830072873754624/2831822349582336/STEM/a1c685e9-e713-4edd-9337-368441bd36b9.png?resizew=285)
(1)求证:
平面
;
(2)若
平面
,试求
的值;
(3)当
是
中点时,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dafebaaf13781120dc57c277d0267c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9a4950a6e4202efd609507964af238b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18091448701460b53e076331e7c575cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://img.xkw.com/dksih/QBM/2021/10/15/2830072873754624/2831822349582336/STEM/a1c685e9-e713-4edd-9337-368441bd36b9.png?resizew=285)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f445af1ae136773cb338920552ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bb178784aa857d4d4683e650273f054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed4cba9d2412e4a28f8740bddd5738d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ad337a2ee42c1d43458859014c54b92.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da17111d46f81cb18e994291fe0786f.png)
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2021-10-18更新
|
397次组卷
|
9卷引用:上海市奉贤中学2021-2022学年高二上学期期中数学试题
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名校
3 . 已知
,若
则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38cd41a999930c01d13f952405662d78.png)
__________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c821115bf1c9f05a45fb5f1ae4622f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da712bc4b03a4ffbc7ce654c39f36854.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38cd41a999930c01d13f952405662d78.png)
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