题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000551-14118.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000551-56718.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000552-20447.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000552-99834.png)
(Ⅰ)在平面ABC内确定一条直线,使该直线与直线CE垂直;
(Ⅱ)判断三棱锥B—CEF的体积是否为定值.若是定值,求出这个三棱锥的体积;若不是定值,说明理由.
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![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000554-90494.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000554-74370.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000555-92114.png)
解析
解: (Ⅰ)取AC中点D,连接BD.
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000555-95698.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000555-63029.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000555-82779.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000556-92154.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000556-36533.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000556-65963.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000556-71024.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000554-74370.png)
(Ⅱ)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000557-47970.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000557-99733.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000557-21468.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000557-25983.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000558-85282.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000558-67266.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000558-95627.png)
由(Ⅰ)可知,
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000558-98840.png)
在等腰三角形ABC中,可求得BD=
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000559-61044.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000559-26547.png)
核心考点
试题【如图,在直三棱柱中,,.棱上有两个动点E,F,且EF = a (a为常数).(Ⅰ)在平面ABC内确定一条直线,使该直线与直线CE垂直; (Ⅱ)判断三棱】;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
(Ⅰ)证明:平面EDC⊥平面SBC.(Ⅱ)求二面角A—DE—C的大小 .
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000519-28094.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000505-57211.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000505-42199.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000505-70845.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000506-19061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000506-42588.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000506-83034.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000506-27519.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000506-65671.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000507-17563.png)
(Ⅰ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000507-60740.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000507-35894.png)
(Ⅱ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000507-52304.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000508-62671.png)
(Ⅲ)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000508-74351.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000445-64508.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000445-51915.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000445-77840.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000446-28624.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000446-17201.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000446-70407.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000446-79358.png)
(Ⅰ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000446-28624.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000446-17201.png)
(Ⅱ)判断四棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000447-44171.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000447-27945.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000447-10028.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000416-89036.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000416-88322.png)
①若
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000416-95272.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000417-37156.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000417-84848.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000417-13100.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000417-92570.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000418-96693.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000418-95073.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000418-66326.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000418-57928.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000418-87574.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000419-23991.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000419-34195.png)
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