题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005657-74963.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005657-11867.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005657-66519.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005657-77979.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005658-90600.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005658-37206.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005658-97164.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005658-83645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005659-78532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005659-22161.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005659-35675.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005700-42686.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005700-79848.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005700-33476.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005657-11867.png)
(2)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005701-67401.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005701-24641.png)
(3)能否在
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005701-10963.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005701-85336.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005702-61891.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005658-90600.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005701-85336.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005702-23901.png)
解析
试题分析:(1)先建立空间直角坐标系,利用法向量证明OD//平面ABC,说明
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005702-43747.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005702-94705.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005703-62838.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005702-23901.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005703-94177.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005703-91459.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005703-98950.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005704-19243.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005704-15807.png)
试题解析:以B为原点,BC为x轴,BA为y轴,BD为z轴,建立空间直角坐标系
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005704-39420.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005704-97210.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005705-66896.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005705-14383.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005705-99077.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005705-33415.png)
(1)平面ABC的法向量
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005702-94705.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005705-82363.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005706-89678.png)
∴OD//平面ABC
(2)设平面ODM法向量为
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005703-62838.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005705-82363.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005706-60621.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005706-79527.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005706-73323.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005702-23901.png)
(3)设EM上一点N满足,
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005707-39154.png)
平面ABDE法向量
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005703-91459.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005703-98950.png)
不存在
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005704-19243.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005704-15807.png)
(传统方法参照给分)
核心考点
试题【如图,平面平面,是等腰直角三角形,,四边形是直角梯形,,,,点、分别为、的中点.(1)求证:平面;(2)求直线和平面所成角的正弦值;(3)能否在上找到一点,使得】;主要考察你对平面的法向量等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005643-75171.jpg)
(1) 证明:BD⊥平面PAC;
(2) 若PA=1,AD=2,求二面角B-PC-A的正切值.
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005619-43354.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005619-71969.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005619-85311.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005620-27031.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005620-55518.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005620-51484.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005620-26134.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005621-91733.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005621-62033.jpg)
(Ⅰ) 求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005621-55522.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005622-79231.png)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005622-57689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005622-68049.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005605-72418.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005606-14662.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005606-90275.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005606-12006.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005606-69340.png)
(2)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005606-48592.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005552-33029.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005553-88027.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005553-38879.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005553-60063.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005553-50007.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005553-21399.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005553-51541.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005554-60088.png)
(Ⅰ)把向量
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005554-35052.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005554-73226.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005554-82523.png)
(Ⅱ)把向量
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005554-13207.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005554-70470.png)
(Ⅲ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005554-42788.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005554-30900.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005554-95393.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005526-19695.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005526-89190.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005527-76808.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005527-66114.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005527-63603.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005526-89190.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005528-71952.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005528-18728.png)
(1)求证:面
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005528-15406.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005527-63603.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005528-39855.png)
(2)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106005528-39682.png)
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