题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005208-60638.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005209-33081.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005209-29691.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005209-90295.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005209-43422.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005210-88225.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005210-70015.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005210-50708.png)
(2)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005210-62906.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005210-50708.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005211-57095.png)
解析
试题分析:(1)直线与平面垂直的证明,对于理科生来说主要是以建立空间直角坐标系为主要方法,所以根据题意建立坐标系后,写出相应的点的坐标.根据向量证明向量
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005211-22473.png)
(2)证明直线与平面所成的角的正弦值,主要是通过求出平面的法向量与该直线的夹角的余弦值,再通过两角的互余关系转化为正弦值.
试题解析:(1)证明:因为
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005211-99526.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005211-97794.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005212-50223.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005212-71582.png)
如图所示,建立空间直角坐标系
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005212-32499.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005213-23827.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005213-58476.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005213-14027.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005213-72974.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005213-63826.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005214-24535.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005214-71791.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005214-92743.png)
又因为
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005214-19554.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005215-97990.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005215-55229.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005215-36914.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005215-98740.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005216-10311.png)
(2)解:由(1)知,
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005216-85021.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005216-10311.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005216-59378.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005216-33393.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005217-14713.png)
设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005217-49673.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005216-10311.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005217-66816.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005217-92939.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005217-14713.png)
所以直线
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005217-19689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005216-10311.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005211-57095.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005153-57594.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005153-19368.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005153-14178.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005153-42731.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005153-33203.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005154-41732.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005154-50239.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005154-83083.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005154-29153.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005154-36844.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005154-98441.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005154-30580.png)
(2)求平面
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005154-88178.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005155-41381.png)
(3)在
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005153-42731.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005155-90596.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005155-70669.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005155-33054.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005155-61345.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005135-87898.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005135-22765.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005135-17580.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005135-22765.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005135-68106.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005135-70020.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005135-55866.png)
(1)求证:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005136-85909.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005136-28901.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005136-28067.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005136-62179.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005124-18856.jpg)
(1)证明:直线EE1∥平面FCC1;
(2)求二面角B-FC1-C的余弦值.
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005111-60190.jpg)
A.![]() | B.![]() | C.![]() | D.![]() |
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