题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035531-91111.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;
(3)在(2)的条件下,求二面角A1-AG-E的大小(文科求其正切值)。
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035531-72781.jpg)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035531-50433.gif)
(2)G是CC1的中点
(3) 故二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035531-29432.gif)
(文)二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035531-29432.gif)
解析
(1)取B1C1的中点E1,连A1E1,E1C,则AE∥A1E1,∴∠E1A1C是异面直线AE与A1C所成的角。设
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035531-85028.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035531-19830.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035531-97132.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035531-59279.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035532-56361.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035532-90717.gif)
所以异面直线AE与A1C所成的角为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035531-50433.gif)
(2).由(1)知,A1E1⊥B1C1,又因为三棱柱ABC-A1B1C1是直三棱柱
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035532-77874.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035532-48860.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035532-80613.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035532-43954.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035532-43954.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035532-38986.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035532-43954.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035533-43684.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035533-77663.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035533-20084.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035533-32386.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035534-28571.gif)
所以G是CC1的中点 ---------------------------- --8分
(3)连结AG,设P是AC的中点,过点P作PQ⊥AG于Q,连EP,EQ,则EP⊥AC.
又
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035532-80613.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035532-43954.gif)
而PQ⊥AG
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035532-43954.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035532-43954.gif)
由EP=a,AP=a,PQ=
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035534-47687.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035534-72262.gif)
所以二面角C-AG-E的平面角是arctan,而所求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035531-29432.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035531-29432.gif)
(文)二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035531-29432.gif)
核心考点
试题【如图,在直三棱柱ABC-A1B1C1中,E是BC的中点。(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;(3)】;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/20191021/20191021035520-43062.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035520-78127.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035520-10803.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035521-60813.gif)
(1)求证:MN∥平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035521-46347.gif)
(2)求点
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035521-61845.gif)
(3)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035521-37711.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035522-28088.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035512-15951.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035512-50716.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035512-80417.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035512-66075.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035513-39562.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035513-27504.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035513-62956.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035513-10860.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035513-27667.gif)
(注意:在试题卷上作答无效)
四棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035458-44110.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035459-77732.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035459-82285.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035459-77732.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035459-97638.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035459-68675.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035500-14812.gif)
(Ⅰ)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035500-96639.gif)
(Ⅱ)设侧面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035500-84243.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035500-87449.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035501-27794.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035448-11443.gif)
⑴求证:平面BEF⊥平面DEF;
⑵求二面角A-BF-E的大小。
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035449-58319.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035427-88663.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035428-75754.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035428-68583.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035428-91013.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035428-70957.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035429-38086.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035429-90819.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035429-64489.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035429-44124.gif)
(Ⅰ)求证:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035429-75186.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035430-92922.gif)
(Ⅱ)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035430-11403.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035430-70931.gif)
(Ⅲ)求点
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035430-77406.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035430-70931.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021035431-15871.jpg)
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