题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055050-45885.png)
给出下列四个命题:①∠BCC1为异面直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055050-19857.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055051-28464.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055051-58088.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055051-13715.png)
答案
解析
试题分析::①∵∠BCC1为120°,而异面直线AD与CC1所成的角为60°,故①错误;
②三棱锥A1-ABD的每个面都为正三角形,故为正四面体,故②正确;
④根据向量加法的三角形法则,
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055051-23326.png)
③
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055052-35303.png)
⑤在三角形ACC1中,
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055052-17982.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055051-58088.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055051-13715.png)
点评:本题考查了异面直线所成的角的定义,直线与平面垂直的定义,正三棱锥的定义,向量加法的三角形法则和数量积运算性质,知识点较为综合,我们应熟练掌握每一个知识点。
核心考点
试题【已知平行六面体ABCD-A1B1C1D1中,∠A1AD=∠A1AB=∠BAD=60°,AA1=AB=AD=1,E为A1D1的中点。给出下列四个命题:①∠BCC1】;主要考察你对线线角等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055045-81900.jpg)
(1)求证:平面O1AC
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055045-94969.png)
(2)求二面角O1-BC-D的大小;
(3)求点E到平面O1BC的距离.
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055032-85364.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055032-96726.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055032-82305.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055032-76580.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055033-94086.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055032-96726.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055033-55034.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055033-72765.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055033-97374.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055034-24710.jpg)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055034-14445.png)
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055034-77673.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055034-11358.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055027-70748.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055027-66191.png)
(1)若F、G分别是AD、BC的中点,且AB∥平面EFG,求证:CD∥平面EFG;
(2)当图1中AE+EC最小时,求图2中二面角A-EC-B的大小.
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055019-42476.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055020-95046.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055020-18805.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055020-38717.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055020-97132.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055021-55954.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055021-55527.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055021-77161.jpg)
(Ⅰ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055021-86714.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055022-50003.png)
(Ⅱ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055020-38717.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055022-16473.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055022-19801.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055022-50003.png)
(Ⅲ)是否存在点
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055020-97132.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055022-67027.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055015-15901.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055016-82962.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055016-32518.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055016-82962.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022055016-51830.png)
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