题目
题型:不详难度:来源:
(Ⅰ)证明:CM⊥SN;
(Ⅱ)求SN与平面CMN所成角的大小.
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012329-42420.jpg)
答案
解析
设PA=1,以A为原点,射线AB,AC,AP分别为x,y,z轴
正向建立空间直角坐标系如图。
则P(0,0,1),C(0,1,0),B(2,0,0),M(1,0,
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012329-41485.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012329-41485.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012329-41485.png)
(Ⅰ)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012330-61497.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012330-98553.png)
(Ⅱ)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012330-67361.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012330-88261.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012331-72647.png)
所以SN与片面CMN所成角为45°。
核心考点
试题【已知三棱锥P-ABC中,PA⊥ABC,AB⊥AC,PA=AC=½AB,N为AB上一点,AB=4AN,M,S分别为PB,BC的中点.(Ⅰ)证明:CM⊥SN;(Ⅱ)】;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/20191022/20191022012325-55547.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012325-30820.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012325-14147.png)
(Ⅰ)求证:AP⊥平面BDE;
(Ⅱ)求直线EB与平面PAC所成的角。
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012325-52357.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012318-89115.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012318-89115.png)
AB=AD=1,DC=SD=2,E为棱SB上的一点,平面EDC
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012318-89115.png)
(Ⅰ)证明:SE=2EB;
(Ⅱ)求二面角A-DE-C的大小 .
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012318-30954.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012311-35540.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012311-32306.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012311-24101.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012312-46483.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012312-38431.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012312-66934.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012312-58867.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012313-66171.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012313-26757.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012313-84652.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012304-57686.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012304-68030.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012304-14249.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012304-23713.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012305-43557.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012305-94731.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012305-56930.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012305-61536.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012306-46570.png)
(1)设
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012306-89551.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012306-92813.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012306-11478.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012306-97064.png)
(2)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012307-18960.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012307-29854.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012307-29533.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012259-22200.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012259-11425.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012300-97029.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022012300-92428.png)
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