名校
1 . 如图,正三棱柱
的所有棱长都为
,
为
中点.试用空间向量知识解下列问题:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/2/54199679-d4fd-4b3a-bd08-5c4657b6bbb6.png?resizew=180)
(1)求证:平面
平面
;
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/2/54199679-d4fd-4b3a-bd08-5c4657b6bbb6.png?resizew=180)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a2e10a5aebe40a9018d5ee3ade7af8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f97babc2abb18c1540d3a5504f7cf3fe.png)
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2019-10-21更新
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347次组卷
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2卷引用:天津市红桥区2016-2017学年高二上学期期中理科数学试题