题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034516-36006.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034516-16377.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034516-69969.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034516-41980.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034516-61885.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034517-77753.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034517-81822.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034517-34628.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034517-82100.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034517-40504.png)
(2)是否存在这样的点
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034516-61885.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034517-52223.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034517-61134.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034517-30420.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034517-42625.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034518-13361.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034518-62237.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034518-73750.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034518-18653.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034518-19098.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034517-82100.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034517-40504.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034518-69173.png)
(2)本小题属于探索性问题,先假设存在点M,使得
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034517-52223.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034517-61134.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034518-65361.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034518-26750.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034517-30420.png)
解:(1)过点M做
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034518-13361.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034518-62237.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034518-73750.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034518-18653.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034518-19098.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034517-82100.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034517-40504.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034519-53220.png)
由题可得:在
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034518-69173.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034519-72661.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034516-16377.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034519-18891.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034519-36191.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034519-19236.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034517-34628.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034517-82100.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034517-40504.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034517-42625.png)
……………………6分
(2)假设存在点M使得
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034517-52223.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034517-61134.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034519-95127.png)
则有
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034518-65361.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034518-26750.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034520-87927.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034520-75891.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034520-10876.png)
所以,当
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034520-23934.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034517-52223.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034517-61134.png)
(向量法:略)
核心考点
试题【(本题满分12分)如图所示,在长方体中,,,,为棱上一点.(1)若,求异面直线和所成角的正切值;(2)是否存在这样的点使得平面?若存在,求出的长;若不存在,请说】;主要考察你对向量与空间位置关系等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034505-64963.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034505-75105.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034505-33518.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034505-12463.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034505-68413.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034506-83547.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034506-89097.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034452-12314.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034452-12314.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034453-24896.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034453-27995.png)
(1)求证:直线PD⊥面ABCD;
(2)求二面角A-PB-D的大小.
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034446-60081.png)
A.AC⊥BD |
B.AC∥截面PQMN |
C.AC=BD |
D.异面直线PM与BD所成的角为45° |
A.平面PAC⊥平面ABC | B.平面PAB⊥平面PBC |
C.PB⊥平面ABC | D.BC⊥平面PAB |
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034430-27194.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034430-77484.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034431-84331.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034431-14633.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034431-62584.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034431-62302.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034432-38172.png)
(1) 求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034432-69549.png)
(2) 求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034432-57057.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034432-38172.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106034433-36907.png)
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