名校
1 . 如图所示,三棱台
的体积为7,其上、下底面均为正三角形,平面
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f2c649fe991df124faaef9dc8876c22.png)
且
,棱
与
的中点分别为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/16/1f91547d-a6a0-4d6c-857d-18dd1a0f824f.png?resizew=229)
(1)证明:
平面
;
(2)求直线
到平面
的距离;
(3)求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/986ba572d8373df48c996f8c8611498c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b7d82423b6f211a7ac51a850b55e73a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f2c649fe991df124faaef9dc8876c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/604f9bbc0657e96ecf3f2e6f47a3c3f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64ddfedec4aab9d2000de0eb6520a936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c0f067a2a348ceb24a408f82992eab8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/16/1f91547d-a6a0-4d6c-857d-18dd1a0f824f.png?resizew=229)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31c34b18525831f3eda7bb90be0199b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1828e73ec5e00f95aa11ff74c703a5c1.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1828e73ec5e00f95aa11ff74c703a5c1.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09d9d486b7f91ba933210dd013a7f2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1828e73ec5e00f95aa11ff74c703a5c1.png)
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