题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040813-55101.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040813-91260.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040814-21114.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040814-22305.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040814-52134.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040814-66637.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040814-37774.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040815-98449.gif)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040815-99287.gif)
又由ABCD是正方形,得:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040815-74491.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040815-95035.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040815-76324.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040816-68019.gif)
(2)延长DC至G,使CG=EB,,连结BG、D1G ,∵CG∥EB ,∴四边形EBGC是平行四边形.
∴BG∥EC. ∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040816-14471.gif)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040816-42841.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040816-61527.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040817-30858.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040817-27548.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040821-12050.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040817-27548.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040821-16623.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040821-60346.gif)
(3)∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040821-83815.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040821-72029.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040821-22559.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040822-22576.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040822-46826.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040822-38686.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040822-52216.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040822-21222.gif)
又由
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040822-11331.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040814-22305.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040822-36826.gif)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040822-66324.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040822-92591.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040823-47941.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040814-22305.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040814-37774.gif)
解法二:(1)见解法一…3分
(2)以D为原点,DA、DC、
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040823-78629.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040823-44726.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040823-14579.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040823-16403.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040823-43176.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040823-13866.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040823-80895.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040821-60346.gif)
(3)设平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040814-22305.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040823-38211.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040824-80190.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040824-48914.gif)
由:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040824-42682.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040823-13866.gif)
可得:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040824-23032.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040824-10441.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040824-63541.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040825-40580.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040825-12492.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040814-22305.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040825-70164.gif)
核心考点
试题【(本小题满分14分)如图,正方体的棱长为2,E为AB的中点.(Ⅰ)求证:(Ⅱ)求异面直线BD1与CE所成角的余弦值;(Ⅲ)求点B到平面的距离.】;主要考察你对空间几何体的结构特征等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040806-56522.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040806-76503.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040806-93932.gif)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040806-74714.gif)
(2)求异面直线EG与BD所成的角;
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040806-82549.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040750-46461.gif)
(Ⅰ)求异面直线PD与BC所成角的余弦值;
(Ⅱ)求二面角P—AB—C的大小;
(Ⅲ)设点M在棱PC上,且
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040750-70444.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040751-82612.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040751-24887.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040736-96202.gif)
(Ⅰ)证明:AM⊥PM ;
(Ⅱ)求二面角P-AM-D的大小;
(Ⅲ)求点D到平面AMP的距离
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040732-15283.gif)
D是AC的中点,
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040732-26740.gif)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040732-87421.gif)
(2)(理科)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040732-63119.gif)
(文科)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021040732-99347.gif)
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