如图,在直三棱柱
中,
,
为线段
的中点.
(Ⅰ)求证:
;
(Ⅱ)若直线
与平面
所成角的正弦值为
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede6a60cad0e0b58e1549fda6e085719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8b8d12608b614ad7e5a8db11505d8d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eda9af121b6d28f2e5edde2df814c64.png)
(Ⅱ)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9d69cf99f3fb9982a4a96aa48e7d235.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19735d76a0967ac4a2c9d147ba4de58e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba564f8149fb98ee50c4012f06708382.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0c640abbdc470479407da1ae2aa80fb.png)
![](https://img.xkw.com/dksih/QBM/2017/8/2/1743616647069696/null/STEM/511b44590a464ddda194e6cae562de0c.png?resizew=113)
更新时间:2017-08-07 18:10:25
|
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解答题-证明题
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适中
(0.65)
【推荐1】如图,在四棱锥
中,四边形
是正方形,
是
的中点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/b5b23f1e-5fa0-4cc7-8a2a-167bdb0e4f8a.png?resizew=155)
(1)求证:
平面
;
(2)若
是线段
上的动点(不含线段端点),当平面
与平面
的夹角为
时,求线段
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/b5b23f1e-5fa0-4cc7-8a2a-167bdb0e4f8a.png?resizew=155)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac09dc1ca2cdd7aef28c218763d3e4d.png)
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【推荐2】已知空间三点
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(1)若
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(2)求
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c39fec21bf3c9ba63980efd9b601e613.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d37ce74c3f50ce2c93c461fb303982b4.png)
(1)若
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b172cf8d898883d82e973f28c3c3a3e.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40436543cc51f42b5b5d93e55a407ce4.png)
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解答题-问答题
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适中
(0.65)
【推荐1】在四棱锥
中,四边形
为菱形,
,且平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/1/bdc3065b-62cd-43fa-a59d-3787b8584795.png?resizew=186)
(1)证明:
平面
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所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/1/bdc3065b-62cd-43fa-a59d-3787b8584795.png?resizew=186)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
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解答题-问答题
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适中
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【推荐2】已知四棱锥P - ABCD的底面为直角梯形,AB∥DC,∠DAB=90°,PA⊥底面ABCD,且PA=AD=DC![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d18b033966094f95339590749b6061f2.png)
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