题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032105-25305.gif)
(1)P、C、D、M四点是否在同一平面内,为什么?
(2)求证:面PBD
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032105-81896.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032105-23616.jpg)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032106-62743.gif)
解析
解(1)P、C、D、M四点不在同一平面内,
反证法:假设P、C、D、M四点在同一平面内,
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032106-91249.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032106-84056.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032106-16666.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032107-97351.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032107-76527.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032107-77356.gif)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032107-93853.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032108-18034.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032108-25268.gif)
又由
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032108-98374.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032108-55351.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032107-77356.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032105-81896.gif)
(3)如图,分别以BA,BC,BP为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032108-49436.gif)
B为原点,建立空间直角坐标系。
则D(2,2,0),P(0,0,2),M(2,0,1)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032109-65815.gif)
设面PMD的法向量
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032109-10184.gif)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032109-62444.gif)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032109-82795.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032109-52831.gif)
直线BD和平面PMD所成的角与
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032110-71135.gif)
所以直线BD和平面PMD所成的角的正弦值为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032106-62743.gif)
核心考点
试题【如图,四边形ABCD是正方形,平面ABCD,MA//PB,PB=AB=2MA=2。(1)P、C、D、M四点是否在同一平面内,为什么?(2)求证:面PBD 面PA】;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/20191021/20191021032059-83371.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032059-83371.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032059-53219.gif)
(1)求PA的长
(2)证明PB
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032059-83371.gif)
(3)求棱PC与平面AMD所成角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032059-17567.gif)
有以下四个命题:
A.平面MB1P⊥ND1; |
B.平面MB1P⊥平面ND1A1; |
C.△MB1P在底面ABCD上的射影图形的面积为定值; |
D.△MB1P在侧面D1C1CD上的射影图形是三角形. |
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032056-78478.gif)
如图,三棱柱
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032039-66951.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032040-70646.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032040-56972.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032040-80332.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032040-29224.gif)
且
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032041-23802.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032041-51112.gif)
(Ⅰ)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032041-88763.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032040-80332.gif)
(Ⅱ)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032041-17576.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032042-68148.gif)
(Ⅲ)在
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032042-81038.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032042-87968.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032042-79876.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032042-68148.gif)
确定点
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032042-87968.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032042-75761.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032035-25905.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032023-33809.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032023-37323.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032023-76553.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032023-97951.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032024-12625.gif)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032024-67075.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032024-16650.gif)
(2)求证:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032024-62682.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032024-60436.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032025-83728.gif)
(3)求四面体
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021032025-42409.gif)
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