如图,在正三棱柱
中,
分别为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/19d73caa-e0f6-4a3a-b2ae-e8efd1564fb6.png?resizew=154)
(1)证明:
平面
;
(2)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b82460802c36cf660ec6b3f6b639f406.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d2d240492190864969a6055620236db.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/19d73caa-e0f6-4a3a-b2ae-e8efd1564fb6.png?resizew=154)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7592c4f01c8e06c7ee90df5b9413a9f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e2f7554a52815bfa0f4d75221ba7397.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41104641f3e2260d00aeadf8fb8a078a.png)
更新时间:2024-02-17 16:05:56
|
相似题推荐
解答题-问答题
|
适中
(0.65)
解题方法
【推荐1】如图,在四面体
中,
,
,且
.
(1)设
为线段
的中点,试在线段
上求一点
,使得
;
(2)求二面角
的平面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99ca6d348c4c0f53eb995246e1cb5ae7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4f2f2404507d03df447404834634ffc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/950e673dc286ecdfa54dc7ab146770b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c53d934a0cd9512e6df17c8f311c3ce4.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b37625595a63cb47e1cdf9c5da40c3e.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fdbc5ac9894f65bf9d25d956158d422.png)
![](https://img.xkw.com/dksih/QBM/2011/7/16/1570260860993536/1570260866187264/STEM/6f757a8c542c42f3b85540c57b8c716a.png?resizew=141)
您最近一年使用:0次
解答题-问答题
|
适中
(0.65)
名校
解题方法
【推荐2】如图,已知三棱柱
,平面
平面
,
,
,
,
,
分别是
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/2c4bff8b-42b3-4ef1-80ff-c6ad5b960491.png?resizew=151)
(1)证明:
;
(2)求直线EF与平面
所成角的余弦值;
(3)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df00cdf77ed39ca5a0b305861a693142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab926d89b65f26c12e3da73ef1e5cf68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70aadc0083a7d87fe96b6b6675ff37c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/2c4bff8b-42b3-4ef1-80ff-c6ad5b960491.png?resizew=151)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc90fee532e50d319081d571410421.png)
(2)求直线EF与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0218542daefa15910d5111b27e71f5b3.png)
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解答题-问答题
|
适中
(0.65)
名校
解题方法
【推荐1】如图,在以
为顶点的五面体中,面
为正方形,
,且二面角
与二面角
都是
.
平面
;
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e63a98f5ed97655875ffb3f9eb413d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6563ec739fe21b2f86aee262be3ec9c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9726261c25e7086835912c0d4815d270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4343d561ca5566c09bccb8f321be0e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c674dc5024374f53920947c4cf4baf11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6240d4cf0fb44aa1e6bdaf2a4bdfb37e.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/325fbf7c39864c58789bc8ebe853dbe9.png)
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解答题-证明题
|
适中
(0.65)
名校
【推荐2】如图,
平面
分别是
上的动点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/23153a98-957c-4a83-a207-a5f0ee02906e.png?resizew=119)
(1)若平面
与平面
的交线为
,求证:
;
(2)当平面
平面
时,求平面
与
平面所成的二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22ccfac02aabbc76292bc97cb13bcb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5346d31f71f5471a0b3e875cacdf7b90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97bde5efa645a4c1ed6874088400d6a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3e1bd91112b2f7a653e012a7df46ac2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/23153a98-957c-4a83-a207-a5f0ee02906e.png?resizew=119)
(1)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29c8cf9c6833b585aa0310713817db40.png)
(2)当平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e51838e395dfc9d9ef597d9e01f46272.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
您最近一年使用:0次