题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112423-69880.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112423-41604.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112423-14352.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112423-81232.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112424-25291.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112424-92599.png)
(2)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112424-54030.png)
(3)求点
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112424-18957.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112424-92599.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112425-42080.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112425-11128.png)
解析
试题分析:(1)由正三棱柱
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112423-69880.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112425-93787.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112425-11313.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112423-14352.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112424-25291.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112424-92599.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112426-44624.jpg)
(2)由平面
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112426-73248.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112426-11148.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112424-54030.png)
(3)点到平面的距离,转化为直线与法向量的关系,再通过解三角形的知识即可得点到平面的距离.本小题关键是应用解三角形的知识.
试题解析:(1)证明:建立如图所示,
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112426-68204.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112426-66850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112427-51552.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112427-53761.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112427-28013.png)
∴AE⊥面A1BD
(2)由
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112427-50951.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112428-64769.png)
设面AA1B的法向量为
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112428-69918.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112428-76224.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112428-33103.png)
由图可知二面角D—BA1—A的余弦值为
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112425-42080.png)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112428-12348.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112429-51991.png)
则B1到平面A1BD的距离d=
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112429-52063.png)
核心考点
试题【如图,正三棱柱所有棱长都是2,D棱AC的中点,E是棱的中点,AE交于点H.(1)求证:平面;(2)求二面角的余弦值;(3)求点到平面的距离.】;主要考察你对空间向量的基本概念等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112356-24118.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112357-84919.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112357-23055.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112357-86817.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112357-64555.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112357-86297.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112357-98843.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112357-15458.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112358-32537.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112358-91344.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112358-47183.jpg)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112359-74580.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112357-84919.png)
(2)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112359-27661.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112359-50326.png)
(3)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112359-70371.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112340-92982.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112340-92982.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112340-71194.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112340-50179.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112341-12976.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112341-79824.jpg)
(1)求证:BC
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112340-92982.png)
(2)求直线AP与平面PDB所成角的正弦值;
(3)设E为侧棱PC上异于端点的一点,
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112341-77147.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112341-12110.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112342-87622.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112328-55195.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112328-26346.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112328-32056.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112328-91961.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112328-97345.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112328-26346.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112328-53772.jpg)
(1)证明:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112329-16880.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112329-85669.png)
(2)若二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112329-10114.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112329-18150.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112329-81297.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112330-52229.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112310-17558.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112310-40307.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112311-51082.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112311-85918.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112311-48873.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112312-74475.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112312-34864.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112312-96505.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112312-10883.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112312-13292.png)
(2)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112313-44065.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112313-55379.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112313-86904.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112305-20213.png)
A.(-2,3,-1) | B.(-2,-3,-1) | C.(2,-3,-1) | D.(-2,3,1) |
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