题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034414-31799.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034414-75110.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034414-29938.gif)
E是CD的中点,PA
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034414-59609.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034415-87202.gif)
(I)证明:平面PBE
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034414-59609.gif)
(II)求二面角A—BE—P和的大小。
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034415-10721.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034415-90058.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034415-46554.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034415-62860.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034415-76619.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034416-54457.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034414-75110.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034414-29938.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034416-99946.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034416-13663.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034416-79837.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034416-69517.gif)
又因为PA
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034414-59609.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034417-85878.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034417-70204.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034417-64067.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034417-80204.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034417-85878.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034414-59609.gif)
(II)由(I)知,
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034417-80204.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034418-83880.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034418-29327.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034418-55584.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034418-22401.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034415-62860.gif)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034419-58847.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034419-83077.gif)
故二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034415-62860.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034415-76619.gif)
解法二:如图所示,以A为原点,建立空间直角坐标系.则相关各点的坐标分别是
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034419-78969.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034419-76963.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034419-11553.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034420-28392.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034420-54877.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034420-77411.gif)
(I)因为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034420-50192.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034421-29988.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034421-97350.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034421-99802.gif)
从而
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034417-80204.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034417-85878.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034414-59609.gif)
(II)易知
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034421-17190.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034421-98071.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034422-89861.gif)
则由
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034422-53745.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034422-60931.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034422-66481.gif)
故可取
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034421-98071.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034423-98203.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034423-60878.gif)
于是,
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034423-70144.gif)
故二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034415-62860.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034415-76619.gif)
核心考点
试题【如图所示,四棱锥的底面是边长为1的菱形,,E是CD的中点,PA底面ABCD,。(I)证明:平面PBE平面PAB;(II)求二面角A—BE—P和的大小。】;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/20191021/20191021034407-54334.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034407-73311.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034407-44016.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034408-37389.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034407-73311.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034407-44016.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034408-37389.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034408-31999.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034408-76941.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034408-42636.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034407-73311.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034407-44016.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034408-37389.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034407-73311.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034408-94929.jpg)
A.![]() | B.![]() |
C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034354-77280.jpg)
如图,在几何体
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034354-98265.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034354-18710.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034355-81151.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034354-18710.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034355-51105.gif)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034355-30114.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034355-24957.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034356-86815.gif)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034356-37089.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034356-41136.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034354-98265.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034348-65121.gif)
⑴求证AE⊥平面BCE;
⑵求二面角B—AC—E的正弦值;
⑶求点D到平面ACE的距离.
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034348-66637.jpg)
如图:在四棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034341-85419.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034342-85547.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034342-24217.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034342-57054.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034342-81325.gif)
(I)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034342-15886.gif)
(II)求三棱锥N
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034343-49217.gif)
(III)在线段PD上是否存在一点E,
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034343-84677.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034343-53271.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034343-75380.jpg)
如图,在直三棱柱ABC-A1B1C1中,
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021034332-40015.gif)
(1)求异面直线AE与A1C所成的角;
(2)若G为C1C上一点,且EG⊥A1C,试确定点G的位置;
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