题目内容
如图1,在直角梯形ABCD中,AB//CD,
E为CD上一点,且DE=4,过E作EF//AD交BC于F现将
沿EF折到
使
,如图2。
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408231655507965301.jpg)
(I)求证:PE⊥平面ADP
;
(II)求异面直线BD与PF所成角的余弦值;
(III)在线段PF上是否存在一点M,使DM与平在ADP所成的角为
?若存在,确定点M的位置;若不存在,请说明理由。
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823165550703781.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823165550734407.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823165550750406.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823165550765493.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408231655507965301.jpg)
(I)求证:PE⊥平面ADP
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/2014082316555081272.gif)
(II)求异面直线BD与PF所成角的余弦值;
(III)在线段PF上是否存在一点M,使DM与平在ADP所成的角为
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823165550843234.gif)
(I)证明略
(II)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823165550859292.gif)
(III)不存在,理由略
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408231655508742748.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823165550921111595.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/2014082316555095262123.jpg)
![](http://thumb2018.1010pic.com/images/loading.gif)
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