题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044440-28337.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044440-75352.gif)
(1)建立适当的坐标系,并写出A、B、A1、C1的坐标;
(2)求AC1与侧面ABB1A1所成的角.
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044440-28337.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044441-66088.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044440-28337.gif)
解析
由已知,得A(0,0,0),B(0,a,0),A1(0,0,
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044440-28337.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044441-66088.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044440-28337.gif)
(2)取A1B1的中点M,于是有M(0,
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044441-25177.gif)
有
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044441-57127.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044441-75729.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044441-92863.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044441-30181.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044440-28337.gif)
由于
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044441-57127.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044441-92863.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044441-57127.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044441-30181.gif)
∴AC1与AM所成的角就是AC1与侧面ABB1A1所成的角.
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044441-80249.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044442-95848.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044442-11758.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044442-11928.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044442-53409.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044442-69033.gif)
核心考点
试题【正三棱柱ABC—A1B1C1的底面边长为a,侧棱长为a.(1)建立适当的坐标系,并写出A、B、A1、C1的坐标;(2)求AC1与侧面ABB1A1所成的角.】;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/20191021/20191021044431-87728.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044431-64340.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044431-34173.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044431-20432.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044431-97672.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044432-55907.png)
(2)设棱
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044432-19941.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044432-71065.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044432-64066.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044432-16762.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044416-60079.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044416-61407.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044416-22595.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044416-18568.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044417-55674.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044417-98325.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044417-34179.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044417-71664.gif)
(I)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044417-73764.gif)
(II)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044418-86839.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044418-28895.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044410-73323.jpg)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044410-51408.gif)
(2)求cos<
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044410-83049.gif)
(3)求证: A1B⊥C1M.
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044354-85108.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044354-47345.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044354-47844.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044354-58505.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044354-89563.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044355-12826.gif)
(I)试在
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044355-10168.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044355-53855.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044355-28802.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044356-91245.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044355-53855.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044356-67765.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044356-17434.gif)
(1)求PC的长;
(2)求异面直线PC与BD所成角的余弦值的大小;
(3)求证:二面角B—PC—D为直二面角.
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021044347-38691.gif)
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