1 . 如图,三棱柱ABC-
中,
⊥平面ABC,AC⊥AB,AB=AC=2,C
=4,D为BC的中点
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/615e79bc-7155-4515-b999-b0d4bcd61f2a.png?resizew=216)
(I)求证:AC⊥平面AB
;
(II)求证:
C∥平面AD
;
(III)求平面
与平面
所成锐二面角的余弦值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/615e79bc-7155-4515-b999-b0d4bcd61f2a.png?resizew=216)
(I)求证:AC⊥平面AB
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a56f2e56229a722d1f40d74d3967a3d.png)
(II)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
(III)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b2213b575a7cfaffcdf91885005c7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
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2 . 如图,在四棱锥P-ABCD中,底面ABCD为正方形,平面PAD⊥底面ABCD,PD⊥AD,PD=AD,E为棱PC的中点
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/4/37910157-d153-450a-b242-9b1c663b3d30.png?resizew=152)
(I)证明:平面PBC⊥平面PCD;
(II)求直线DE与平面PAC所成角的正弦值;
(III)若F为AD的中点,在棱PB上是否存在点M,使得FM⊥BD?若存在,求
的值,若不存在,说明理由.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/4/37910157-d153-450a-b242-9b1c663b3d30.png?resizew=152)
(I)证明:平面PBC⊥平面PCD;
(II)求直线DE与平面PAC所成角的正弦值;
(III)若F为AD的中点,在棱PB上是否存在点M,使得FM⊥BD?若存在,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754a74bf749ce5f8edbc831f8d303bed.png)
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