题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070136-45129.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070136-48463.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070136-43970.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070136-95349.png)
求证:(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070136-10735.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070136-63460.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070136-52689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070137-66131.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070136-45129.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070137-77931.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070137-21744.png)
所以,
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070137-21013.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070136-48463.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070138-40547.png)
所以,
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070138-17348.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070138-73119.png)
所以,
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070136-10735.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070138-44178.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070138-79906.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070139-26881.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070139-89048.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070139-39711.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070138-73119.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070139-89048.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070139-26881.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070136-43970.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070136-95349.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070139-39711.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070139-60920.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070140-86705.png)
又因为
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070140-51360.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070136-52689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070140-41715.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070136-52689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070136-63460.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070140-89079.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070136-52689.png)
解析
核心考点
举一反三
A.![]() | B.![]() | C.![]() | D.1 |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070125-70421.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070125-63653.png)
A.![]() | B.![]() | C.![]() | D.![]() |
①直线AD与直线B1P为异面直线;
②恒有A1P∥面ACD1;
③三棱锥A-D1PC的体积为定值;
④当且仅当长方体各棱长都相等时,面PDB1⊥面ACD1.
其中所有正确命题的序号是
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070120-66263.png)
A.32 | B.![]() | C.48 | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070116-90127.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070109-34680.png)
(I)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070109-96278.png)
(II)求点E到平面ACD的距离;
(III)求二面角A—CD—B的余弦值。
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022070109-50228.jpg)
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