题目内容
(本小题满分12分)如图所示,已知六棱锥
的底面是正六边形,
平面
,
是
的中点。
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240040316808771.png)
(Ⅰ)求证:平面
//平面
;
(Ⅱ)设
,当二面角
的大小为
时,求
的值。
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824004031602703.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824004031618394.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824004031633469.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824004031649400.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824004031664367.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240040316808771.png)
(Ⅰ)求证:平面
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824004031696422.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824004031711546.png)
(Ⅱ)设
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824004031711571.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824004031727658.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824004031742402.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824004031758292.png)
(Ⅰ)只需证OM//PD, BE//DC;(Ⅱ)
.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824004031774487.png)
试题分析:(Ⅰ)连接AD交BE与点O,连接OM,因为
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824004031649400.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824004031664367.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824004031805644.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824004031696422.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824004031711546.png)
(Ⅱ)以A为原点,AE、AB、AP所在直线分别为
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824004031852464.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824004031852372.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240040318673071.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240040318832802.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824004031898770.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824004031914781.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240040319301965.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240040319452653.png)
因为二面角
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824004031727658.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824004031742402.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240040319761868.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824004031774487.png)
点评:用向量法求二面角,优点是思维含量少,确定是计算较为复杂。因为我们再用向量法求二面角时,一定要认真、仔细。避免出现计算错误。
![](http://thumb.zyjl.cn/images/loading.gif)
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