题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113744-68317.png)
(1)求证BC⊥平面AFG;
(2)求二面角B-AE-D的余弦值.
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113744-18146.png)
解析
试题分析:(1)折叠问题,首先要明确折叠前后量的变化,尤其是垂直条件的变化,本题要证明线面垂直,首先找线线垂直,折叠前后都有条件
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113744-58671.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113744-77525.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113745-36401.png)
试题解析:(1) 在图甲中,由△ABC是等边三角形,E,D分别为AB,AC的三等分点,点G为BC边的中点,易知DE⊥AF,DE⊥GF,DE//BC. 2分
在图乙中,因为DE⊥AF,DE⊥GF,AF
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113745-98541.png)
又DE//BC,所以BC⊥平面AFG. 4分
(2) 因为平面AED⊥平面BCDE,平面AED
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113745-98541.png)
以点F为坐标原点,分别以FG,FD,FA所在的直线为
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113745-60511.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113745-90329.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113746-47574.jpg)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113746-76159.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113746-38211.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113746-91143.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113747-13945.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113747-24462.png)
设平面ABE的一个法向量为
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113747-20090.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113747-31641.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113748-12356.png)
取
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113748-73935.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113748-88830.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113748-10716.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113749-75336.png)
显然
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113749-20445.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113745-36401.png)
二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113749-56051.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113749-56051.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113744-18146.png)
核心考点
试题【如图甲,△ABC是边长为6的等边三角形,E,D分别为AB、AC靠近B、C的三等分点,点G为BC边的中点.线段AG交线段ED于F点,将△AED沿ED翻折,使平面A】;主要考察你对空间向量的基本概念等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113734-36002.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113734-10184.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113734-57030.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113734-77983.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113734-66654.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113735-17881.png)
(1)求证:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113735-10540.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113735-84274.png)
(2)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113735-96245.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113726-52389.jpg)
A.![]() ![]() | B.2+![]() |
C.![]() ![]() | D.![]() ![]() |
A.(9,0,16) | B.25 |
C.5 | D.13 |
A.1个 | B.2个 | C.不存在 | D.无数个 |
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113712-65324.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113712-49845.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113712-33554.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113712-29166.png)
A.(![]() ![]() ![]() | B.(![]() ![]() ![]() |
C.(![]() ![]() ![]() | D.(![]() ![]() ![]() |
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