题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013734-93158.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013734-89539.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013735-81461.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013735-92045.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013735-78108.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013735-35401.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013735-54627.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013736-78139.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013736-98815.gif)
(Ⅰ)证明:直线
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013736-41742.gif)
(Ⅱ)求异面直线AB与MD所成角的大小;
(Ⅲ)求点B到平面OCD的距离。
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013736-94597.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013736-10436.gif)
(1)取OB中点E,连接ME,NE
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013737-85515.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013737-20745.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013737-50834.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013737-60053.gif)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013737-54872.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013738-83793.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013738-61212.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013738-39135.gif)
作
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013738-89078.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013738-33958.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013739-89329.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013739-29462.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013739-57437.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013739-28273.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013738-61212.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013738-39135.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013740-73898.gif)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013740-25575.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013740-64279.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013740-68786.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013740-56540.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013741-57437.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013741-58325.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013741-38001.gif)
所以点B到平面OCD的距离为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013741-49483.gif)
方法二(向量法)作
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013741-36434.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013742-63403.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013742-94110.gif)
(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013742-14574.gif)
设平面OCD的法向量为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013742-62218.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013743-35853.gif)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013743-99171.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013743-62655.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013743-21368.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013743-19917.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013737-50834.gif)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013738-61212.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013738-39135.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013744-13490.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013744-71421.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013744-64790.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013738-61212.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013738-39135.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013740-73898.gif)
(3)设点B到平面OCD的距离为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013744-87283.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013744-87283.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013745-32633.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013743-21368.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013745-93926.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013745-76361.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013741-49483.gif)
解析
核心考点
试题【 (本小题满分12分)如图,在四棱锥中,底面四边长为1的菱形,, ,,为的中点,为的中点(Ⅰ)证明:直线;(Ⅱ)求异面直线AB与MD所成角的大小; (Ⅲ)求点B】;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/20191021/20191021013717-75248.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013717-36278.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013717-56416.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013717-42611.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013717-98283.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013718-74066.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013718-61579.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013718-96530.gif)
(Ⅰ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013718-56671.gif)
(Ⅱ)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013718-58907.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013719-43948.gif)
(Ⅲ)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013717-36278.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013719-16787.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013719-87732.jpg)
如图,已知
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013704-99325.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013704-96543.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013705-82942.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013705-61589.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013705-11256.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013705-50277.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013705-18366.gif)
(1)求证:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013705-59589.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013706-59097.gif)
(2)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013706-87719.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013706-49076.gif)
如图,已知
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013647-33789.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013647-55803.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013648-25346.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013648-44403.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013648-37200.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013648-12045.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013649-34892.gif)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013649-54504.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013649-51762.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013649-75547.gif)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013650-14955.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013650-31427.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013650-59208.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013648-44403.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013650-88332.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013642-99403.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013642-11299.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013642-91101.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013642-25561.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013642-12276.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013642-11299.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013643-37528.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013643-69029.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013643-97907.gif)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013643-64808.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013643-90850.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013644-69753.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013644-32962.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013644-50964.gif)
(2)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021013644-49965.gif)
点D到面SBC的距离等于
A.![]() | B.![]() | C.![]() | D.![]() |
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