名校
1 . 如图,在四棱锥
中,平面
平面
,
,
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2021/5/11/2718627252404224/2719709336920064/STEM/0c75e768-3696-4432-8c6e-1dbc6a71b9b8.png)
(1)求证:
平面
;
(2)求直线
与平面
所成角的正弦值;
(3)在棱
上是否存在点
,使得平面
与平面
所成的锐二面角余弦值为
?若存在,求
的值;若不存在、说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5732edb0ebc901cc220dca71f96775d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62974d34de3a12418d6b700420afd1b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/958330f56d75b05fbf9144e6fd458be4.png)
![](https://img.xkw.com/dksih/QBM/2021/5/11/2718627252404224/2719709336920064/STEM/0c75e768-3696-4432-8c6e-1dbc6a71b9b8.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(3)在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f239fbcc58fc15535db4b5084c4f7253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69d048ac0c9b13b54417c2e2de17082b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f32f82942e12701f6ba4b87d02291b1.png)
您最近一年使用:0次
21-22高二上·浙江·期末
名校
2 . 如图,在四棱锥
中,
,面
面
,M为
的中点.
![](https://img.xkw.com/dksih/QBM/2021/5/6/2715478096633856/2715717048090624/STEM/d76f136a01df41fc8528567427fa3c21.png?resizew=188)
(Ⅰ)求证:
;
(Ⅱ)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abd98da18aa05708c279a0fabcbc6f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3abb27f8d654064a92f9d7a11e586ab5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ee10bfa63ab58c5027bc0af0c0d016f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccaee8f228ff24e7c89879bb5b999cf2.png)
![](https://img.xkw.com/dksih/QBM/2021/5/6/2715478096633856/2715717048090624/STEM/d76f136a01df41fc8528567427fa3c21.png?resizew=188)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7aaccd4f94fac8096a6cf70d94eb589.png)
(Ⅱ)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
您最近一年使用:0次
2021-05-07更新
|
2547次组卷
|
6卷引用:广西南宁市第三中学2021届高三二模数学(理)试题
广西南宁市第三中学2021届高三二模数学(理)试题陕西省汉中市2022届高三上学期第一次教学质量检测理科数学试题陕西省汉中市2022届高三教学质量第一次检测考试理科数学试题(已下线)【新东方】高中数学20210429—002【2020】【高二上】(已下线)专题05 空间向量与立体几何(重点)-2020-2021学年高二数学下学期期末专项复习(北师大版2019选择性必修第一册、第二册)(已下线)专题01 空间向量与立体几何的典型题(一)-【尖子生专用】2021-2022学年高二数学考点培优训练(人教A版2019选择性必修第一册)
名校
解题方法
3 . 如图,在三棱柱
中,
平面
分别为
的中点,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc9b17d5fe8e039d5de1f195b7202778.png)
![](https://img.xkw.com/dksih/QBM/2021/4/22/2705354688331776/2713098799767552/STEM/5067447b-2f9c-4cdc-867c-7f985c8bfbd3.png?resizew=226)
(1)求证:
平面
;
(2)求二面角
的正弦值;
(3)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8bfe2553e852df73185d017c0a62fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be8e413b6b062029ec08a51ba604b5fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2efe30b0b1a3b0c49b4fa58b7cce943b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc9b17d5fe8e039d5de1f195b7202778.png)
![](https://img.xkw.com/dksih/QBM/2021/4/22/2705354688331776/2713098799767552/STEM/5067447b-2f9c-4cdc-867c-7f985c8bfbd3.png?resizew=226)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e59b1f7689bff6644bfdeb9e36feb163.png)
(3)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
您最近一年使用:0次
2021-05-03更新
|
1593次组卷
|
3卷引用:天津市河西区2021届高三下学期总复习质量调查(二)数学试题
名校
解题方法
4 . 如图,在三棱柱
中,
,
,四边形
是菱形,
,平面ABB1A1⊥平面ABC,点
是
中点,点
是
上靠近
点的三等分点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/0367339c-fbc9-4a69-b811-46dbd0403ca0.jpg?resizew=207)
(1)证明:
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b10134e7a46e6f6f7cb9d5e2371727d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86cab6037cdd25b50d219550046a37fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/0367339c-fbc9-4a69-b811-46dbd0403ca0.jpg?resizew=207)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4b5068a142c39664e25539d27be030b.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8035fc825a001d7d9a3dacd8271662.png)
您最近一年使用:0次
2021-06-03更新
|
1553次组卷
|
6卷引用:百师联盟2021届高三冲刺卷(二)新高考卷数学试题
百师联盟2021届高三冲刺卷(二)新高考卷数学试题(已下线)7.5 空间向量求空间角(精讲)-【一隅三反】2022年高考数学一轮复习(新高考地区专用)(已下线)秘籍06 空间向量与立体几何(理)-备战2022年高考数学抢分秘籍(全国通用)(已下线)专题19 空间几何解答题(理科)-1浙江省绍兴市鲁迅中学2022-2023学年高二普通班上学期期末模拟数学试题江西省宜春市宜丰县宜丰中学2022-2023学年高二上学期第三次月考(12月)数学试题
名校
解题方法
5 . 如图,在三棱台
中,平面
平面
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/15/83b8014c-02df-4a43-9e41-b484d60eb8b8.png?resizew=189)
(1)证明:
;
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/986ba572d8373df48c996f8c8611498c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b7d82423b6f211a7ac51a850b55e73a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f3bd47ca6cc94b6b642a57c299dcfc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09c57d4c6ddf04ef6eaa2987378b434b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/15/83b8014c-02df-4a43-9e41-b484d60eb8b8.png?resizew=189)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13d28cb7181257cf732af4b615fc47d.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc6bc85b019e9d158ca1d92feed796e.png)
您最近一年使用:0次
2021-09-12更新
|
1253次组卷
|
3卷引用:第34讲 利用坐标法解决立体几何的角度与距离问题-2022年新高考数学二轮专题突破精练
(已下线)第34讲 利用坐标法解决立体几何的角度与距离问题-2022年新高考数学二轮专题突破精练重庆市第十八中学2020-2021学年高二下学期3月月考数学试题广东省深圳市布吉中学2021-2022学年高二上学期期中数学试题
解题方法
6 . 如图,在三棱锥
中,
底面
.点D,E,N分别为棱
的中点,M是线段
的中点,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/4a950e55-c57f-47d5-8d2c-ea4312f94609.png?resizew=201)
(Ⅰ)求证:
平面
;
(Ⅱ)求二面角
的正弦值;
(Ⅲ)已知点H在棱
上,且直线
与直线
所成角的余弦值为
,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9177a42f9ab232822de2b889a572932.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55928df632fc6f2b88a44afe37e5a4e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/119d2453d9262756ef3be3b4b52a762c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/4a950e55-c57f-47d5-8d2c-ea4312f94609.png?resizew=201)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(Ⅱ)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3f1c2d75dc63c9669f3b7b0e1a2ff4.png)
(Ⅲ)已知点H在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff9d2abf13c2842f58654abf73c6b4ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b94ab384ee86aed107af8b3bbb1d13b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826c728050e3378921442ace20269ef6.png)
您最近一年使用:0次
名校
解题方法
7 . 如图所示,在四棱台
中,
底面
,四边形
为菱形,
,
.
![](https://img.xkw.com/dksih/QBM/2021/3/15/2678680104845312/2684215312261120/STEM/1561cd34-00ff-46d2-9f21-7959cb76d236.png?resizew=248)
(1)若
为
中点.求证:
平面
;
(2)求直线
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eee296a7d9fba487f1485c61580196f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/293cdfa41786bfd10ac7a4e92769dab0.png)
![](https://img.xkw.com/dksih/QBM/2021/3/15/2678680104845312/2684215312261120/STEM/1561cd34-00ff-46d2-9f21-7959cb76d236.png?resizew=248)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0edb1508fc95765f3bb316bcb5252d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
您最近一年使用:0次
名校
8 . 已知正方形的边长为4,
、
分别为
、
的中点,以
为棱将正方形
折成如图所示的60°的二面角,点
在线段
上.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/16/eeed4286-85b4-4cee-b444-913d2056bcd8.png?resizew=355)
(1)若
为
的中点,且直线
与由
,
,
三点所确定平面的交点为
,试确定点
的位置,并证明直线
平面
;
(2)是否存在点
,使得直线
与平面
所成的角为60°?若存在,求线段
的长,若不存在,请说明理由.
![](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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/16/eeed4286-85b4-4cee-b444-913d2056bcd8.png?resizew=355)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907d5147cea4c9ce855074864fe54506.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6072ec6dfc0203cabb1fe289a5ddc8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/558ce69401f3c97930f00ba0e2aa6647.png)
(2)是否存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/558ce69401f3c97930f00ba0e2aa6647.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
您最近一年使用:0次
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9 . 如图,在三棱柱
中,点E,F分别在棱
,
上(均异于端点),
,
,
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/31/5e3a0c86-a33d-40dd-8b75-8cd8c5393f2c.png?resizew=260)
(1)求证:四边形
是矩形;
(2)若
,
,求平面
与平面
所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fbec5434bcf9173dfeebd92aa0c5070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dba9cf66066aafbafb6116928eeb10ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d25e8fc3dda4f8b45491514b6e22a962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/31/5e3a0c86-a33d-40dd-8b75-8cd8c5393f2c.png?resizew=260)
(1)求证:四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6480f384476190883f06c0289c7519.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c4599c8c996873814673237b8942df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d9e036eecc9aebcc2d2a2855bbfafdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
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2021-09-18更新
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1741次组卷
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4卷引用:湖北省新高考九师联盟2021届高三下学期2月质检巩固数学试题
湖北省新高考九师联盟2021届高三下学期2月质检巩固数学试题(已下线)专题04 二面角(含探索性问题)-【解题思路培养】2022年高考数学一轮复习解答题拿分秘籍(全国通用版)四川省内江市第六中学2022届高三下学期考前强化训练二数学(理科)试题黑龙江省哈尔滨市第三中学2021-2022学年高二上学期10月月考数学试题
名校
10 . 如图1,在平行四边形
中,
=60°,
,
,
,
分别为
,
的中点,现把平行四边形
沿
折起如图2所示,连接
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/3/b8e39710-99eb-4ef5-abe1-9a672673aa4c.png?resizew=396)
(1)求证:
;
(2)若
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883732ae71bfed76e07732ec709f4653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b5d693c4f0c4d0e6c0c810e7d464b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883732ae71bfed76e07732ec709f4653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa6cb992b6faad4744f85d73a3b76dd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a56f2e56229a722d1f40d74d3967a3d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/3/b8e39710-99eb-4ef5-abe1-9a672673aa4c.png?resizew=396)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82c2b3adb41e8965f553da2e5086a751.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a677b42f8b427b21924a559b90141d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c44507c93f6180afd1697d2fa5a5c741.png)
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2021-06-15更新
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1645次组卷
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12卷引用:2016届福建福州市高三上学期期末数学(理)试卷
2016届福建福州市高三上学期期末数学(理)试卷2017届河南南阳一中高三理上学期月考四数学试卷宁夏石嘴山市第三中学2017届高三下学期第三次模拟考试数学(理)试题河南省南阳市2018届高三期终质量评估数学(理)试题广西南宁二中2020届高三4月开学考试理数试题四川省成都市实验外国语学校2020届高三(高2017级)数学模拟(三)理试题(已下线)专题19 立体几何综合-2020年高考数学(理)母题题源解密(全国Ⅲ专版)湖北省武汉一中2021届高三下学期二模数学试题(已下线)2022年高考考前20天终极冲刺攻略(三)【理科数学】 (5月27日)广东省广州市广州大学附属中学2021-2022学年高二上学期第一次月考数学试题广东省真光中学2021-2022学年高二上学期10月月考数学试题2023版 北师大版(2019) 选修第一册 突围者 第三章 专项拓展训练3 用空间向量解决折叠问题