题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150731-38202.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150732-11740.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150732-95322.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150732-11740.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150732-13926.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150732-39721.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150733-32211.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150733-98360.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150733-34256.gif)
(I)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150734-15418.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150734-37094.gif)
(Ⅱ)求三棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150734-71586.gif)
(Ⅲ)求平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150734-37094.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150735-92794.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150735-22243.jpg)
答案
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150735-18260.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150736-51140.jpg)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150736-96884.jpg)
在正三角形BCD中,BE=EC,
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150736-86809.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150736-54508.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150737-54558.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150737-69193.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150737-19653.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150737-62072.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150738-10765.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150738-56940.gif)
(Ⅱ)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150738-60714.gif)
且
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150738-14850.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150739-27713.gif)
(Ⅲ)证法一:如图建立空间直角坐标系
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150739-14529.gif)
则由(I)知平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150734-37094.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150740-35717.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150740-79225.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150740-84312.gif)
设平面PBC的法向量为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150740-63920.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150741-80965.gif)
取
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150741-79635.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150741-67847.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150742-20687.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150742-11846.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150742-66207.gif)
证法二:由(I)知
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150742-44943.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150743-17264.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150743-93301.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150742-11846.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150743-16530.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150743-93301.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150744-10059.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150744-15545.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150744-24791.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150744-51199.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150735-92794.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150742-11846.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150745-12430.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150743-93301.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150745-11600.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150734-37094.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150735-92794.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150742-11846.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150745-95707.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150746-56988.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150746-70794.gif)
核心考点
举一反三
(Ⅰ)若D为AA1中点,求证:平面B1CD⊥平面B1C1D;
(Ⅱ)若二面角B1-DC-C1的大小为60°,求AD 的长。
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150724-95463.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150708-56945.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150708-74649.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150708-68971.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150708-39457.gif)
(1)求三棱锥C-ABE的体积;
(2)在CD上是否存在一点M,使得MO//平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150709-41651.gif)
证明你的结论.
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150709-46092.gif)
已知 ∠
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150657-52664.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150657-25616.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150657-84139.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150657-53111.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150658-91275.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150658-87985.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150658-62018.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150644-12793.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150644-58318.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150644-62902.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150645-70224.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150645-76555.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150645-10545.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150645-27008.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150645-32739.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150646-52774.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150646-96187.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150646-52114.jpg)
(I)要使矩形
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150644-58318.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150646-52183.gif)
(II)当
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150646-52183.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150644-58318.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150624-65650.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150624-89358.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150624-65260.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150625-62994.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150625-95677.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150624-65260.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150625-21809.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150625-33850.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150624-65260.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150625-22627.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150626-80151.gif)
(Ⅰ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150626-66232.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150626-45910.gif)
(Ⅱ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150626-67479.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150627-98435.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150627-19969.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150627-98745.gif)
(Ⅲ)求四棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021150627-68686.gif)
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