题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004628-47454.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004628-47454.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004628-15910.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004628-72045.png)
(2)若AC=1,求直线AM与平面VAC所成角的大小.
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004629-40638.jpg)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004629-40646.png)
解析
试题分析:(1)证明直线与平面垂直的关键是证明该直线与平面内两条相交直线都垂直;(2)求直线与平面所成角的关键是找出直线在平面内的射影,进而构造直角三角形,求出线面角.
试题解析:(1)∵
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004628-15910.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004629-52299.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004629-57582.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004629-52299.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004629-74822.png)
∵点C为
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004628-47454.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004630-94522.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004630-68136.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004630-52844.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004628-72045.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004630-14764.jpg)
(2)如图,取VC的中点N,连接MN,AN,则MN∥BC
由(1)得,BC⊥平面VAC
∴MN⊥平面VAC
∴∠MAN为直线AM与平面VAC所成的角 9分
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004630-54149.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004631-61010.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004631-60277.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004631-63202.png)
∴直线AM与平面VAC所成角的大小为
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004631-57841.png)
核心考点
试题【如图,已知的直径AB=3,点C为上异于A,B的一点,平面ABC,且VC=2,点M为线段VB的中点.(1)求证:平面VAC;(2)若AC=1,求直线AM与平面VA】;主要考察你对线线角等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004555-28680.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004555-71696.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004555-74227.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004555-18746.png)
(1) 求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004555-97326.png)
(2) 若直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004555-20641.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004555-95767.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004555-75729.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004555-76313.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004556-87781.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004537-75168.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004537-21602.png)
(2)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004537-48310.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004538-20207.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022004530-42296.png)
(1)求证:AN∥平面 MBD;
(2)求异面直线AN与PD所成角的余弦值;
(3)求二面角M-BD-C的余弦值.
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