题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232002-52425.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232003-96276.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232003-10504.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232003-72739.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232003-29406.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232004-84584.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232004-90770.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232004-94946.png)
(1)求棱
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232004-77241.png)
(2)求点
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232005-88444.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232005-93418.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232005-42137.png)
解析
试题分析:解:(1)设
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232005-20817.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232005-86320.png)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232006-11460.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232006-76583.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232006-52186.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232004-77241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232006-20888.png)
(2)以点
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232005-88444.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232007-52741.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232007-81163.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232007-65958.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232007-39459.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232007-66470.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232008-68994.png)
由已知及(1),可知
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232008-63682.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232008-77425.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232008-48134.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232009-88872.png)
设平面
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232005-93418.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232009-59468.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232009-10827.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232009-89874.png)
其中
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232010-11894.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232010-97104.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232010-90378.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232010-74634.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232011-26510.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232011-74963.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232011-65405.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232011-21457.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232011-52205.png)
在平面
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232005-93418.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232003-72739.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232012-53850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232005-88444.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232005-93418.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020232005-42137.png)
点评:求点到平面的距离,可通过向量方法来求解,有时也可通过三棱锥的体积来求解(等体积法)。
核心考点
试题【在长方体中,,过、、三点的平面截去长方体的一个角后,得到如图所示的几何体,且这个几何体的体积为.(1)求棱的长;(2)求点到平面的距离.】;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/20191020/20191020231953-29445.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231953-93015.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231954-62294.jpg)
(1)求异面直线
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231954-71480.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231954-80102.png)
(2)求多面体
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231954-87409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231943-35791.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231943-79719.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231943-29473.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231943-84439.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231943-44262.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231943-69008.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231943-34497.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231944-82592.png)
(1) 证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231944-42939.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231943-44262.png)
(2) 求四棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231943-35791.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231944-78808.png)
几何体EFG —ABCD的面ABCD,ADGE,DCFG均为矩形,AD=DC=l,AE=
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231926-19520.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231926-12817.png)
(I)求证:EF⊥平面GDB;
(Ⅱ)线段DG上是否存在点M使直线BM与平面BEF所成的角为45°,若存在求等¥
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231927-30205.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231913-29244.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231913-67333.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231913-58591.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231904-82843.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231904-26442.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231905-37342.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231905-74912.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020231905-16152.png)
(Ⅰ)求证:平面PCD⊥平面PAC;
(Ⅱ)求四棱锥P—ACDE的体积.
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