题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050513-11413.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050514-65374.png)
(1) 求证:DE⊥AC
(2)求DE与平面BEC所成角的正弦值
(3)直线BE上是否存在一点M,使得CM//平面ADE,若存在,求M的位置,不存在,请说明理由。
答案
则
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050514-32671.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050514-33611.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050514-92497.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050515-34502.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050515-98270.png)
故:DE⊥AC(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050515-60025.png)
解析
试题分析:以A为原点,以射线AB,AC,AE为坐标轴建立空间直角坐标系,
则
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050514-32671.png)
由C作平面ABD的垂线,垂足为F,则F为BC的中点,
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050514-33611.png)
所以点C的坐标为
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050514-92497.png)
(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050515-34502.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050515-16537.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050515-36693.png)
设平面BCE的法向量为
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050516-92263.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050516-22350.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050516-10894.png)
设线面角为
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050516-91013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050516-46036.png)
(3)设
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050517-13811.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050517-12036.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050517-48628.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050517-27329.png)
点评:采用空间向量的方法求解立体几何问题的步骤:建立空间直角坐标系,写出相关点及相关向量的坐标,将坐标代入证明或计算求解的对应公式求解,空间向量法要求学生数据处理时认真仔细
核心考点
试题【如图,将边长为2的正方形ABCD沿对角线BD折叠,使的平面ABD⊥平面CBD,AE⊥平面ABD,且AE=,(1) 求证:DE⊥AC(2)求DE与平面BEC所成角】;主要考察你对线线角等知识点的理解。[详细]
举一反三
①若
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050503-21379.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050503-90168.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050504-62054.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050504-27242.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050504-48296.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050504-82455.png)
③若
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050505-36952.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050503-90168.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050504-82455.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050505-93998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050504-48296.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050504-62054.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050505-52792.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050505-74615.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050506-71993.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050506-52487.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050449-51692.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050449-81321.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050449-97488.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050449-28851.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050449-86731.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050449-17099.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050449-47120.jpg)
(Ⅰ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050450-29951.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050449-81321.png)
(Ⅱ)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050450-34867.png)
(Ⅲ)在线段
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050450-78885.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050450-30323.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050449-86731.png)
面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050450-32067.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050450-58000.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050450-30323.png)
若不存在,请说明理由.
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050436-61512.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050436-67499.png)
A.若![]() ![]() ![]() | B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() | D.若![]() ![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050416-67592.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050416-56234.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050416-38350.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050416-82644.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050417-82746.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050417-17838.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050417-29246.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050417-77158.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050417-15409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050418-19610.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050418-28268.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050418-43220.png)
(1)求双曲线的离心率;
(2)过双曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050417-77158.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050418-27768.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050418-41765.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050418-10372.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050419-97199.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050419-79115.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022050419-70347.png)
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