题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120210-45949.png)
(1)当点M是EC中点时,求证:BM//平面ADEF;
(2)当平面BDM与平面ABF所成锐二面角的余弦值为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120210-43016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120210-93618.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120210-81501.png)
解析
试题分析:以
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120210-31292.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120210-74167.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120211-27181.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120211-46083.png)
(1)要证
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120211-16121.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120211-97220.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120211-27805.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120211-97220.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120211-35186.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120211-97144.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120211-99707.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120211-23208.png)
利用向量的数量积求得
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120211-58203.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120212-81701.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120212-33384.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120212-40988.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120212-15849.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120212-26771.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120212-92292.png)
试题解析:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120212-14089.jpg)
(1)以
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120210-31292.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120210-74167.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120211-27181.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120211-46083.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120212-70363.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120212-85020.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120211-97220.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120212-40962.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120212-90684.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120211-16121.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120211-97220.png)
(2)依题意设
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120211-97144.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120211-99707.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120211-23208.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120212-28186.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120213-69455.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120213-66101.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120211-58203.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120212-81701.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120212-33384.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120213-56427.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120213-15405.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120213-99118.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120213-50046.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120213-86906.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120213-30411.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120213-24213.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120213-14088.png)
核心考点
试题【如图,正方形ADEF与梯形ABCD所在平面互相垂直,AD⊥CD,AB//CD,AB=AD=,点M在线段EC上且不与E、C垂合.(1)当点M是EC中点时,求证:B】;主要考察你对柱锥台的表面积等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120149-45913.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120149-20421.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120150-67052.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120150-35556.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120150-50321.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120150-26465.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120140-40287.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120137-95907.png)
A.12π cm3 | B.36π cm3 | C.![]() | D.![]() |
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