题目
题型:不详难度:来源:
如图,已知
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025613-83576.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025613-42461.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025613-40504.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025613-42149.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025614-84648.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025614-74472.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025614-68711.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025614-39466.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025614-45543.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025615-44430.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025615-72134.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025615-40771.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025615-44430.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025615-53504.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025616-80063.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025616-63438.gif)
(Ⅰ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025616-47232.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025616-80063.gif)
(Ⅱ)求折后直线DN与直线BF所成角的余弦值;
(Ⅲ)求三棱锥N—ABF的体积.
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025616-89828.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025616-47232.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025616-80063.gif)
(Ⅱ)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025617-80941.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025617-47388.gif)
(Ⅲ)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025617-34324.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025617-48691.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025618-25286.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025618-11079.gif)
则平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025618-96662.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025616-80063.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025618-26259.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025618-60121.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025616-80063.gif)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025615-53504.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025616-80063.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025619-56211.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025615-53504.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025616-80063.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025616-63438.gif)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025615-53504.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025616-80063.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025619-63802.gif)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025616-47232.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025616-80063.gif)
(Ⅱ)法一.如图,建立空间直角坐标系,
∵在原图中AB=6,∠DAB=60°,
则BN=
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025619-93548.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025619-93548.gif)
∴N(0,
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025619-93548.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025619-16875.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025620-25290.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025619-93548.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025620-77125.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025619-93548.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025617-80941.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025617-47388.gif)
∴折后直线DN与直线BF所成角的余弦值为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025620-49336.gif)
法二.在线段BC上取点M,使BM=BF,则MN∥BF
∴∠DNM或其补角为DN与BF所成角.
又MN=BF=2,DM=
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025620-55794.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025620-19274.gif)
∴折后直线DN与直线BF所成角的余弦值为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025620-49336.gif)
(Ⅲ)∵AD∥EF, ∴A到平面BNF的距离等于D到平面BNF的距离,
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025617-34324.gif)
即所求三棱锥的体积为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025621-33985.gif)
核心考点
试题【(本小题12分)如图,已知为平行四边形,,,,点在上,,,与相交于.现将四边形沿折起,使点在平面上的射影恰在直线上.(Ⅰ)求证:平面;(Ⅱ)求折后直线DN与直线】;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/20191021/20191021025609-65057.gif)
①若
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025609-97625.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025609-62505.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025610-52193.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025610-24168.gif)
其中正确命题的个数是 ( )
A.0 | B.1 | C.2 | D.3 |
如图(1)是一正方体的表面展开图,MN 和PB 是两条面对角线,请在图(2)的正方体中将MN 和PB 画出来,并就这个正方体解决下面问题。
(1)求证:MN//平面PBD;
(2)求证:AQ⊥平面PBD;
(3)求二面角P—DB—M 的大小.
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025601-67266.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025552-77285.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025552-84409.png)
A.若![]() | B.若![]() ![]() |
C.若![]() | D.若![]() |
如图的多面体是底面为平行四边形的直四棱柱
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025541-69307.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025541-69447.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025541-41987.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025542-92967.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025542-58857.gif)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025542-17239.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025542-37453.gif)
(2)求平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025541-69447.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025543-62929.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025543-21445.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025537-13724.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025537-29201.gif)
①
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025537-46280.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025537-70580.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025537-59325.gif)
③
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025538-38280.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025538-60132.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025538-84131.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021025538-65011.gif)
其中正确命题的序号是( )
A.①②③ | B.②③④ | C.①③ | D.②④ |
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