题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010900-80729.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010900-80704.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010900-69505.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010900-16445.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010900-86007.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010901-42420.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010901-95850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010901-93964.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010901-68548.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010901-53541.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010901-72779.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010901-99823.jpg)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010902-40046.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010900-80704.png)
(2)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010902-97945.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010902-19720.png)
(3)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010902-93821.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010902-52073.jpg)
则A(0,0,0),E(0,4,2),F(2,2,0),B(4,0,0),
B1(4,0,4),D(2,0,2), …………(2分)
(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010902-87969.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010902-78409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010902-72714.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010902-94180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010902-21733.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010903-87722.png)
∴DE∥平面ABC. …………(4分)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010903-98040.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010903-35784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010903-89824.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010903-69087.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010903-88871.png)
(3) 平面AEF的法向量为
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010903-58040.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010903-50976.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010904-61038.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010904-38769.png)
令x=2,则
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010904-31680.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010904-30544.png)
∴二面角B1—AE—F的余弦值为
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010905-45214.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010905-17688.jpg)
解析
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010839-26192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010839-79675.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010839-52147.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010839-21742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010839-47812.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010839-33908.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010839-52147.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010840-45096.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010840-88074.png)
(Ⅰ)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010840-86401.png)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010840-64435.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010840-49320.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010840-46625.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010840-41049.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010831-38188.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010831-91297.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010831-42940.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010831-44555.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010831-58436.png)
(1)求证:对任意的
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010831-28051.png)
(2)若二面角C-AE-D的大小为
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010831-53067.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010831-43086.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010831-23333.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010819-46228.png)
(2)求直线PC与底面ABCD所成角
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010819-27659.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010820-10413.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010809-12928.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010809-23163.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010809-51818.png)
(1)求证:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010810-39776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010810-60314.png)
(2)求点A到平面BEF的距离;
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106010810-46423.png)
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