2011·北京西城·一模
1 . 如图,
是边长为
的正方形,
平面
,
,
,
与平面
所成角为
.
![](https://img.xkw.com/dksih/QBM/2015/9/25/1572241494597632/1572241500585984/STEM/c2dd45c4ba1646c69e090be9382caaf5.png)
(Ⅰ)求证:
平面
;
(Ⅱ)求二面角
的余弦值;
(Ⅲ)设点
是线段
上一个动点,试确定点
的位置,使得
平面
,并证明你的结论.
![](https://img.xkw.com/dksih/QBM/2015/9/25/1572241494597632/1572241500585984/STEM/fe701b53575443c292db4d872e40ef05.png)
![](https://img.xkw.com/dksih/QBM/2015/9/25/1572241494597632/1572241500585984/STEM/2a3e33d681e842f8b71707d3b573487c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05638d82225327da27e5f916d2d4e747.png)
![](https://img.xkw.com/dksih/QBM/2015/9/25/1572241494597632/1572241500585984/STEM/fe701b53575443c292db4d872e40ef05.png)
![](https://img.xkw.com/dksih/QBM/2015/9/25/1572241494597632/1572241500585984/STEM/4ff673aaecc44d63acbd5c98d6eac0a3.png)
![](https://img.xkw.com/dksih/QBM/2015/9/25/1572241494597632/1572241500585984/STEM/527f9ac3d51e4280b1e8f14331835f42.png)
![](https://img.xkw.com/dksih/QBM/2015/9/25/1572241494597632/1572241500585984/STEM/b0a0b01103ed4e7b9373b12fcb75fef5.png)
![](https://img.xkw.com/dksih/QBM/2015/9/25/1572241494597632/1572241500585984/STEM/fe701b53575443c292db4d872e40ef05.png)
![](https://img.xkw.com/dksih/QBM/2015/9/25/1572241494597632/1572241500585984/STEM/7ae9bad96345493fb94386207d35553e.png)
![](https://img.xkw.com/dksih/QBM/2015/9/25/1572241494597632/1572241500585984/STEM/c2dd45c4ba1646c69e090be9382caaf5.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/599b63c003aeb99d777e87182db8f019.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(Ⅱ)求二面角
![](https://img.xkw.com/dksih/QBM/2015/9/25/1572241494597632/1572241500585984/STEM/8162eff6ad1c42db89028790e9e2fb4f.png)
(Ⅲ)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac480d8d9d7821b62a603cf5cfda236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
您最近一年使用:0次
2014·北京房山·一模
名校
2 . 如图,三棱柱
中,
平面
,
,
,
,以
,
为邻边作平行四边形
,连接
和
.
![](https://img.xkw.com/dksih/QBM/2014/5/12/1571712601071616/1571712607068160/STEM/625373d6-e844-43c7-a40f-acb2883d026f.png?resizew=193)
(Ⅰ)求证:
平面
;
(Ⅱ)求直线
与平面
所成角的正弦值;
(Ⅲ)线段
上是否存在点
,使平面
与平面
垂直?若存在,求出
的长;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ad3a578f403b9e6b97fa2dc955fc11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e75d14708e6aa1404477db9d7e3166f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2eb89294b31ffdd2680b4361e8994d7.png)
![](https://img.xkw.com/dksih/QBM/2014/5/12/1571712601071616/1571712607068160/STEM/625373d6-e844-43c7-a40f-acb2883d026f.png?resizew=193)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4ac809549102844f24d73a5bfdf2464.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
(Ⅱ)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee3d1518e197f7f25c341da6b1e3483.png)
(Ⅲ)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee3d1518e197f7f25c341da6b1e3483.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ee076fe7dbca5616c4e8a6869a355f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
您最近一年使用:0次
2016-12-03更新
|
5895次组卷
|
3卷引用:2014届北京市房山区4月高三一模理科数学试卷