题目
题型:不详难度:来源:
![](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)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112330-64198.png)
解析
试题分析:(1)可以遵循思路面面垂直
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112330-56129.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112330-56129.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112330-32619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112330-32619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112330-32619.png)
(2)求线面夹角可以利用三维空间直角坐标系,分别以DA,DB,PD三条两两垂直的直线建立坐标系,求面法向量与直线的夹角的余弦值的绝对值即为线面夹角的余弦值.
试题解析:
(1)∵
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112330-21076.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112331-34814.png)
又∵
![](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/20191105/20191105112331-57822.png)
又∵
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112331-78075.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112331-79214.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112329-85669.png)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112332-82001.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112330-52229.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112329-16880.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112329-85669.png)
(1)由(1)所证,
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112331-79214.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112329-85669.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112329-85669.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112329-85669.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112332-33637.png)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112328-91961.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112332-15660.png)
分别以
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112332-59176.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112333-82574.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112333-66966.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112333-77733.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112333-63415.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112334-87705.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112334-33550.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112334-81745.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112334-42901.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112335-49896.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112335-13802.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112335-34862.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112335-47242.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112330-52229.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112336-57574.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112336-41743.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112336-32911.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112336-57689.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/20191105/20191105112337-49893.png)
核心考点
举一反三
![](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) |
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112244-43300.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112244-26962.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112244-31786.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112244-84288.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112245-22934.jpg)
(1)求证:AE⊥平面BCD;
(2)求二面角A–DC–B的余弦值.
(3)在线段
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112245-57800.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112245-98907.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112246-66156.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112246-18768.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112246-86855.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112230-25073.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112230-29490.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112230-15485.png)
是矩形,
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112230-34682.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112230-23483.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112230-52750.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112231-81030.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112231-84073.png)
(2)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112231-59787.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112231-41103.png)
(3)若平面
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112230-15485.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112231-86134.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112231-49954.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112231-62625.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112231-98558.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112232-50249.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112203-93476.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112204-29724.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112204-79109.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112204-20448.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112204-49111.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112204-25522.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112204-87100.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112205-17756.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112205-64146.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112205-20725.png)
(1)求异面直线
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112205-10541.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112205-10541.png)
(2)求几何体
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112203-93476.png)
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