名校
1 . 如图,三棱台
中,
,
是
的中点,点
在线段
上,
,平面
平面
.
(1)证明:
;
(2)若平面
平面
,
,
,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/986ba572d8373df48c996f8c8611498c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5545dc3211671941048034af38092fa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6813b47d087578bf054bcf56b64b42a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b25bc6d842432f74f18c2a92cdc14e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d59f321362853cd5473f306fa17fd92a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/27/a62df7cd-5e58-4114-8acb-6725bb1b3b66.png?resizew=164)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9f6079d1b0033b46fe2909ea602d1e5.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcc97cc47a65c900c7ff295c5e7e576d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/822ba132ca9dd0d4a050659aef3c9b26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f19c369389fa3bfa23de98ffd7b4037c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/193b5b41994c2a4dfa5bb0bc984061cc.png)
您最近一年使用:0次
2023-05-26更新
|
1062次组卷
|
4卷引用:福建省龙岩第一中学2023届高三第六次模拟数学试题
福建省龙岩第一中学2023届高三第六次模拟数学试题山东省聊城市2023届高三三模数学试题江苏省扬州市高邮中学2023届高考前热身训练(二)数学试题(已下线)专题06 立体几何 第一讲 立体几何中的证明问题(分层练)
名校
解题方法
2 . 四棱锥
底面为平行四边形,且
,
,
,
平面
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/13/d4b935ce-18d0-41e4-a140-fbee167a6f87.png?resizew=156)
(1)棱
上是否存在点
,使
平面
?若存在,求
的值;若不存在,请说明理由.
(2)若异面直线
与
所成角的余弦值为
,求平面
与平面
所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05740f0c6071846227dc0ec177ad15e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b99a0a946fda95212b6f5b8970810c2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/13/d4b935ce-18d0-41e4-a140-fbee167a6f87.png?resizew=156)
(1)棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30067b7b236d17af8a462f96a58d11bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1885efcff0b903e314057dd153578600.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/029311a3f1755463a88b69a5e3c9a539.png)
(2)若异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/802e162b98c280720fcb909cf392fda3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c745df4f226027778d5fe45b6501b822.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
2022-09-11更新
|
816次组卷
|
2卷引用:福建省上杭第一中学2023届高三(实验班)上学期暑期考试数学试题
名校
解题方法
3 . 如图,在四棱锥P-ABCD中,PA⊥底面ABCD,AD∥BC,∠DAB=90°,AB=BC=
=2,E为PB的中点,F是PC上的点.
(2)求点C到平面PBD的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c605f428994894bf0b0d9f066ac7495c.png)
(2)求点C到平面PBD的距离.
您最近一年使用:0次
2022-10-04更新
|
587次组卷
|
15卷引用:2020届福建连城县第一中学高三4月模拟考试数学(文)试题
2020届福建连城县第一中学高三4月模拟考试数学(文)试题五岳(湖南、河南、江西)2019-2020学年高三下学期3月线上联考数学(文)试题2五岳(湖南、河南、江西)2019-2020学年高三下学期3月线上联考数学(文)试题12020届河南省高三4月第三次在线网上联考文科数学2020届河南省高三下学期第三次(4月份)联考(文科) 数学试题2020届宁夏银川市第九中学高三下学期第二次模拟考试数学(文)试题吉林省通钢一中、集安一中、梅河口五中等省示范高中2020届高三(5月份)高考数学(文科)模拟试题江西省贵溪市实验中学2020-2021学高二上学期期中考试数学(理)试题江西省贵溪市实验中学2020-2021学年高二12月月考理科数学试题四川省泸州市江阳区2021-2022学年高三上学期期末数学文科试题河南省中原名校联盟2021-2022学年高二上学期第二次适应性联考理科数学试题(已下线)第03讲 直线、平面平行垂直的判定与性质(讲)江苏省南京市金陵中学2022-2023学年高二上学期10月月考数学试题江西省赣州市赣县第三中学2022-2023学年高二上学期期中测试数学试题湖南省永州市第一中学2023-2024学年高一下学期5月月考数学试卷
名校
解题方法
4 . 如图,四棱锥
中,底面
为矩形,侧面
为等腰直角三角形,
,
,F是
的中点,二面角
的大小为120°,设平面
与平面
的交线为l.
![](https://img.xkw.com/dksih/QBM/2021/3/5/2671277929529344/2672706906169344/STEM/d423e7e4-4ae8-468b-8790-d5760c5787c5.png)
(1)在线段
上是否存在点E,使
平面
?若存在,确定点E的位置;若不存在,请说明理由;
(2)若点Q在l上,直线
与平面
所成角的正弦值为
,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d923a338dd2d2e29336b42574d38448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e2aa19d543b5ba5bcc93a34f5432d8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4155f313a2a5b634f83de8a6b1f1596d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d923a338dd2d2e29336b42574d38448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21665d21bbfb04410c78345de1fd15ae.png)
![](https://img.xkw.com/dksih/QBM/2021/3/5/2671277929529344/2672706906169344/STEM/d423e7e4-4ae8-468b-8790-d5760c5787c5.png)
(1)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9df740160690029ac1e730c85f20347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84b156bc439fbaba3bfc9937beccb9b2.png)
(2)若点Q在l上,直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c550269f3199038726f55cbd281c13a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/802e162b98c280720fcb909cf392fda3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3525ddc5153fada64eaf14e50b536542.png)
您最近一年使用:0次
2021-03-07更新
|
488次组卷
|
3卷引用:福建省龙岩市2021届高三下学期第一次教学质量检测数学试题
福建省龙岩市2021届高三下学期第一次教学质量检测数学试题(已下线)专题02 立体几何中存在性问题的向量解法-【重难点突破】2021-2022学年高二数学上册常考题专练(人教A版2019选择性必修第一册)江苏省五校(南师大附中,邗江一中,瓜州中学,公道中学等)2022-2023学年高三上学期期末联考数学试题
名校
5 . 如图,在四棱锥
中,
底面
,
,
,
,
为
的中点,
是
上的点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/27/451cc2a0-0951-4e68-b5b2-6c689f0a3720.png?resizew=184)
(1)若
平面
,证明:
平面
.
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06f8b31977748e6c8e53b4536f1c4dc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/27/451cc2a0-0951-4e68-b5b2-6c689f0a3720.png?resizew=184)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f445af1ae136773cb338920552ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caa431d661bf9f419e8ab713dd4a3c80.png)
您最近一年使用:0次
2020-03-28更新
|
505次组卷
|
3卷引用:2020届福建连城县第一中学高三4月模拟考试数学(理)试题