题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041204-94425.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041205-41520.png)
(1)求证:A1E//平面D1AP
(2)求直线AP与平面
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041205-11317.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041205-58028.png)
答案
因为A1F//D1P,所以A1F//平面D1AP……………2分
又因为EF//BC1//AD1,所以EF//平面D1AP…………4分
A1F ∩EF=F,,所以平面A1EF//平面D1AP
又由于A1E在平面A1EF内,
因此A1E//平面D1AP…………………………………6分
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041206-27760.jpg)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041206-90810.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041206-85046.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041206-49476.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041206-49301.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041207-43632.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041207-48617.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041207-91512.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041208-58311.png)
所以,直线AP与平面
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041205-11317.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041208-66129.png)
解析
核心考点
试题【(本题14分)如图,在棱长为1的正方体中,E,P分别是侧棱B1C1,上的中点(1)求证:A1E//平面D1AP(2)求直线AP与平面所成角的正切值】;主要考察你对向量与空间位置关系等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041150-69808.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041150-41927.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041151-44624.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041151-21281.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041150-41927.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041151-10342.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041151-43171.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041152-44768.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041152-70725.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041152-70288.png)
(2)求平面
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041152-23126.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041152-71962.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041152-73157.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041143-31944.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041144-62329.png)
(1)求证:DE⊥PC;
(2)求直线PD与平面BCDE所成角正弦值;
(3)求点D到平面PBC的距离.
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041137-28967.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041137-35001.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041138-43947.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041138-17426.png)
A.垂直于平面![]() ![]() |
B.垂直于直线![]() ![]() |
C.垂直于平面![]() ![]() |
D.垂直于直线![]() ![]() ![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041129-12678.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041129-13563.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041129-20759.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041129-25019.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041129-32280.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041129-58937.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041129-25019.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041129-32280.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041129-92248.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041129-59386.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041129-53649.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041130-32216.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041107-16480.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041107-63735.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041107-52874.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041107-66708.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041108-78551.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041108-93403.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041108-77856.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041108-47748.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041108-98462.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041108-69093.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041108-54233.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041108-34148.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041107-16480.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041109-41536.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041109-34342.png)
(Ⅰ)求证:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041109-22041.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041107-16480.png)
(Ⅱ)若以
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041109-56001.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041109-72858.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041109-38885.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041108-93403.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041109-47180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041109-47180.png)
(Ⅲ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041109-47180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041109-56769.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106041109-19704.jpg)
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