题目
题型:不详难度:来源:
A.90° | B.60° | C.45° | D.30° |
答案
解析
由正方体的几何特征可得A1B∥CD1,
故∠BA1E即为异面直线A1E与CD1所成角
设正方体ABCD-A1B1C1D1的棱长为2,
则在△A1BE中,A1B=2
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022011918-96038.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022011918-96038.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022011918-96038.png)
故cos∠BA1E=(A1B2+A1E 2-BE2) /(2A1B•A1E) =
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022011919-61118.png)
故∠BA1E=30°
故选D
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022011912-21351.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022011912-78445.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022011912-99285.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022011912-65469.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022011913-73013.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022011907-78718.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022011907-78718.png)
∠ACB=60°,则∠BCF等于 。
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022011849-81102.jpg)
(Ⅰ)求证:EF⊥平面PBC;
(Ⅱ)求二面角F-PC-B的平面角的余弦值.
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022011841-11355.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022011841-28606.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022011841-70337.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022011822-83598.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022011822-73012.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022011822-15576.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022011822-13739.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022011823-69275.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022011823-38500.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022011823-10193.png)
(2)、当
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022011823-14004.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022011824-44623.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022011824-32587.png)
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