名校
解题方法
1 . 如图,已知正三棱柱
的所有棱长都为2,
为
中点,试用空间向量知识解下列问题:
![](https://img.xkw.com/dksih/QBM/2020/5/25/2470338876768256/2470433363509248/STEM/84180d596611465680a90f4df0f72fe3.png?resizew=220)
(1)求
与
所成角的余弦值;
(2)求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.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/2020/5/25/2470338876768256/2470433363509248/STEM/84180d596611465680a90f4df0f72fe3.png?resizew=220)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4560fa4ad459b58b723c74bd24e51ebf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
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