题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113355-16984.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113355-59231.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113356-32558.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113356-21464.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113356-37601.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113356-25123.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113356-19101.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113356-49012.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113356-96371.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113356-90055.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113355-16984.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113356-35553.jpg)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113357-75723.png)
(2)若二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113357-23595.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113357-54177.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113357-49485.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113357-65909.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113357-87545.png)
解析
试题分析:(1)在
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113357-50980.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113357-81623.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113358-47069.png)
再利用
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113358-76615.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113358-61340.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113358-77222.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113358-61340.png)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113358-73723.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113358-83888.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113358-42439.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113358-91758.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113358-42439.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113359-57218.png)
(2)建立空间直角坐标系,利用“空间向量方法”得到
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113359-35878.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113359-88202.png)
试题解析:(1)证明:在
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113357-50980.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113359-11145.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113357-81623.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113359-42863.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113358-47069.png)
又因为
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113358-76615.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113358-61340.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113358-77222.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113358-61340.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113358-73723.png)
又因为
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113359-47434.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113358-83888.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113358-42439.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113358-91758.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113358-42439.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113359-57218.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113359-33703.jpg)
(2)因为
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113358-76615.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113358-61340.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113358-47069.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113359-54327.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113359-75035.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113400-48826.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113400-63429.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113400-24048.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113400-45197.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113400-53484.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113400-49601.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113401-20920.png)
设平面
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113401-67080.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113401-93779.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113401-60406.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113402-32989.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113402-81325.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113402-11387.png)
又平面
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113402-14613.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113402-28394.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113359-35878.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113359-88202.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113357-65909.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113357-87545.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113320-41131.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113320-97720.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113320-63964.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113320-71435.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113321-59411.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113321-51923.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113321-53526.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113321-86483.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113322-65898.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113322-44094.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113322-59735.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113322-49867.png)
(2)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113323-32215.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113311-46455.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113311-78766.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113311-21514.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113312-39930.jpg)
A.![]() |
B.直线![]() ![]() |
C.直线![]() ![]() ![]() |
D.二面角![]() ![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113306-71746.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113307-91398.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113306-71746.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113306-71746.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113307-91398.png)
A.-3 | B.1 | C.-3或1 | D.3或1 |
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113258-34197.png)
(1)求证:直线BD⊥平面OAC;
(2)求直线MD与平面OAC所成角的大小;
(3)求点A到平面OBD的距离。
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113246-65641.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113246-10133.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113246-10133.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113246-31366.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113246-69508.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113246-57218.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113246-78507.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113246-69538.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113247-78398.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113247-75975.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113246-31366.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113247-38985.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113247-11246.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113247-25937.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113247-97809.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113247-61116.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113247-10374.png)
(2)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113247-62346.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105113248-96013.png)
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