题目
题型:不详难度:来源:
如图3,已知正三棱柱
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081011-28077.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081012-53186.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081012-96327.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081012-45759.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081012-75786.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081012-68011.gif)
(Ⅰ)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081013-58783.gif)
(Ⅱ)求点
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081013-46732.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081013-24651.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081013-93263.gif)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081014-29343.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081014-45916.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081014-94580.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081014-98940.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081014-41581.gif)
过E作
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081015-47451.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081015-49502.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081015-38364.gif)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081015-67298.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081015-86258.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081016-35717.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081016-96896.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081016-54700.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081016-99047.gif)
故二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081016-35717.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081016-13318.gif)
(Ⅱ)由(Ⅰ)知
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081017-68857.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081017-67039.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081017-92949.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081017-50691.gif)
过
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081018-55509.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081018-59374.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081018-68769.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081018-98696.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081017-50691.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081018-55702.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081019-14528.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081017-50691.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081019-74482.gif)
解法二:(Ⅰ)求侧棱长
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081019-23713.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081019-63312.gif)
取BC中点E , 如图建立空间直角坐标系
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081020-21215.gif)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081020-38364.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081020-56575.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081020-40559.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081020-74281.gif)
|
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081021-51155.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081017-50691.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081021-39500.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081021-15863.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081021-88607.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081022-79002.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081022-44227.gif)
即二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081016-35717.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081022-55906.gif)
(Ⅱ)∵
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081022-65261.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081019-14528.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081017-50691.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081022-69945.gif)
解析
核心考点
举一反三
四棱柱ABCD—A1B1C1D1
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081007-78797.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081007-52966.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081007-78797.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081007-42153.gif)
(Ⅰ)确定点G的位置,使
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081007-14844.gif)
(Ⅱ)求二面角F—CE—C1的余弦值。
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081003-18047.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081003-18047.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081004-56293.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081004-56293.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080959-36562.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081000-77947.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081000-77947.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081000-27974.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081000-24860.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081000-27974.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081000-64200.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081001-34834.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081001-97376.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080959-36562.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081000-77947.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022081000-27974.gif)
如图,已知
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080941-41430.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080941-50551.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080941-49510.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080941-19754.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080941-55004.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080942-29603.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080942-44217.gif)
(Ⅰ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080942-37234.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080942-17260.gif)
(Ⅱ) 若
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080943-18047.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080943-64419.gif)
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