![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408231814460291876.gif)
解:(1)∵平面ABCD
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823181445888559.gif)
.
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/2014082318144606073.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823181446075457.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823181446091800.gif)
∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/2014082318144606073.gif)
MD
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823181445935414.gif)
------------2分
(2) 分别以DA,DC,DM为x轴,y轴,z轴建立空间直角坐标系,则A(2,0,0), N(2,0,2),E(1,2,0),D(0,0,0), C(0,2,0), F(0,0,1), ------4分
则
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823181446153810.gif)
设平面NDE的法向量是
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823181446169502.gif)
则
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408231814461851005.gif)
,
取b="1. " 则
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823181446200492.gif)
------------6分
∴点A到平面NDE的距离是
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823181446231754.gif)
。----------7分
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823181446247539.gif)
,
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823181446263702.gif)
,
∴ CF∥平面NDE。------------10分
(3)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823181446278561.gif)
是面AND的法向量,
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823181446294969.gif)
。------------12分
∵ 二面角E-ND-A为锐角------------13分
∴ 二面角E-ND-A的平面角大小的余弦值为
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823181446309217.gif)
。---------14分