名校
解题方法
1 . 三棱台
中,若
平面
,
,
,
,M,N分别是
,
中点.
平面
;
(2)求二面角
的正弦值;
(3)求点C到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ecf072589c0f901d92f6bda111d841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f90e17995e2f71e297d94ae51c7e5b1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9260ee90b4107dcdc5b2b0937c40e8c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dea2ae9d515f9ab351ad72306b776ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c7f53b79ef0f0206a55fdf5a3cbfd76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a3f5c4436466bed86c25c5f26ccbeb.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f699aaec89f6fcf1efd8810a6be90e0c.png)
(3)求点C到平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a3f5c4436466bed86c25c5f26ccbeb.png)
您最近一年使用:0次
2024-03-12更新
|
2009次组卷
|
5卷引用:天津市武清区杨村第一中学2024届高考数学热身训练卷
名校
解题方法
2 . 如图,在四棱锥
中,底面
为直角梯形,
,
平面
,
,点
分别在线段
和
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/23/5c17bde0-fa82-4bb8-8437-1017c48a654e.png?resizew=164)
(1)求证:
平面
;
(2)求平面
与平面
夹角的正弦值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/405effb49ef901476701e72cc47918da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f95475bfc06e884754eb4a455c3f434e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e8412dfb48302532531d77e589fb5ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/23/5c17bde0-fa82-4bb8-8437-1017c48a654e.png?resizew=164)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c7c261740ac2ae26715e1298ca278a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab5f236e0c248607721ff77b6ea8b6ee.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab5f236e0c248607721ff77b6ea8b6ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b81fb655624ff75a5eab94de9b8c8e9.png)
您最近一年使用:0次
2024-01-09更新
|
677次组卷
|
2卷引用:天津市武清区河西务中学2023-2024学年高二上学期第三次统练数学试卷
名校
解题方法
3 . 如图,已知
平面
,
为矩形,
,M,N分别为线段
,
的中点.
平面
;
(2)求
与平面
所成角的正弦值.
(3)若Q是线段
的中点,求点Q到平面
的距离.
![](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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5ef03497414d454933f76684ee16970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7592c4f01c8e06c7ee90df5b9413a9f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c5757f787d98f9a46777324b69ad672.png)
(3)若Q是线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c5757f787d98f9a46777324b69ad672.png)
您最近一年使用:0次
2024-01-05更新
|
1338次组卷
|
4卷引用:天津市武清区杨村一中2024届高三上学期第三次质量检测数学试题
天津市武清区杨村一中2024届高三上学期第三次质量检测数学试题北京市丰台区怡海中学2023-2024学年高二上学期期末模拟练习数学试题(2)(已下线)专题13 空间向量的应用10种常见考法归类(3)(已下线)信息必刷卷04(天津专用)
4 . 如图,已知
垂直于梯形
所在的平面,矩形
的对角线交于点
,
为
的中点,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/2/21a81918-58a2-4108-8b58-c237bd3343bc.png?resizew=184)
(1)求证:
平面
;
(2)求平面
与平面
夹角的余弦值;
(3)在线段
上是否存在一点
,使得
与平面
所成角的大小为
?若存在,求出
的长;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc6fd59aca9984b6e13354749339823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/666c7e13a7999bd5970c1e478a665935.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cbf1f67d0542548aee22300554922e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/2/21a81918-58a2-4108-8b58-c237bd3343bc.png?resizew=184)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/debdc6632a4877e5131d3da25cda8b89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffee8b7eff437080a0936d837ceabe95.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef796b46e68fe77b117ff0483d2370c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c25254dc72dbcde9dba272507539e301.png)
(3)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcdae78f4d3b8d8213ac3ac9a9567eb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef796b46e68fe77b117ff0483d2370c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
您最近一年使用:0次
5 . 四棱锥
中,底面
为正方形,
,
面
,
分别为
的中点,直线
与
相交于O点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/2/34a0436b-d522-48c4-8eb9-2eda685c9d7a.png?resizew=159)
(1)证明:
平面
;
(2)求直线
与平面
所成角的正弦值;
(3)求平面
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f83a04565a8ebaa111894b724b0ba266.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/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0d87f681c57a2e1fd7efead6280a3f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/2/34a0436b-d522-48c4-8eb9-2eda685c9d7a.png?resizew=159)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30067b7b236d17af8a462f96a58d11bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b7c70f0668aa9683f08b021bc219d05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/862efecdb6efec5e9ecb73c7230e84e3.png)
您最近一年使用:0次
名校
解题方法
6 . 如图,在圆锥
中,底面圆
的半径为2,线段
是圆
的直径,顶点
到底面的距离为
,点
为
的中点,点
是底面圆上的一个动点,且不与A,B重合.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/18/01d8f98d-885c-4890-83df-642b376db44e.png?resizew=150)
(1)证明:直线
平面
;
(2)若二面角
的余弦为
,
(i)求线段
的长;
(ii)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/18/01d8f98d-885c-4890-83df-642b376db44e.png?resizew=150)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8c2b786c64e6a9ed2ec5670cde74f86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08452588675f76da2f8d31387b3a8224.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167e4b949f6bda469c5ac4af5a85a0db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3aace91caec728e174daec29a3568ae.png)
(i)求线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
(ii)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68cc7dc4e1e3c7ec5ecda50a696eb50a.png)
您最近一年使用:0次
2023-12-18更新
|
348次组卷
|
2卷引用:天津市武清区英华实验学校2024届高三上学期第二次月考数学试题
7 . 如图,在三棱锥
中,PA⊥平面ABC,AB⊥BC,E,F,M分别为AP,AC,PB的中点,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee442383c56eea63a7ab6fa39332010.png)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cdf6198a6b0ad5c3b11d0eb3f660c60.png)
(2)求直线EF与AB所成角的余弦值;
(3)求平面PAC与平面PBC夹角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc2aaed1e9ead175f30f7130569d0411.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee442383c56eea63a7ab6fa39332010.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/15/91473723-3601-4a22-b6fd-3ff5aa6e0624.png?resizew=139)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cdf6198a6b0ad5c3b11d0eb3f660c60.png)
(2)求直线EF与AB所成角的余弦值;
(3)求平面PAC与平面PBC夹角的大小.
您最近一年使用:0次
解题方法
8 . 如图,
且
,
,
且
,
且
,
平面
,
,M是AB的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/8/5adf0929-b1c9-462c-9fec-4e576de708e9.png?resizew=161)
(1)若
求证:
平面DMF;
(2)求直线EB与平面DMF所成角的正弦值;
(3)若在DG上存在点P,使得点P到平面DMF的距离为
,求DP的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aabb9d68cfb70f66bb7a52c2e961dd10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdc143c7fd7c471ca91b6ccc22438fdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6121c4ae264961f49bc9008b0e9ca9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fee573ad62dc536a05dadf5008f1afb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/755d575f0a87f3345e232b66d5956070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cf187bc2ede965870b90757b495f53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81b091ee5a8b32424b2b836dde7860c7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/8/5adf0929-b1c9-462c-9fec-4e576de708e9.png?resizew=161)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1029496e181d2aba81bae248d9e05dd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f214481e6b23307a37940f6dd0313d30.png)
(2)求直线EB与平面DMF所成角的正弦值;
(3)若在DG上存在点P,使得点P到平面DMF的距离为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc269b2ccd1cc42c7036eaf1ecc519e2.png)
您最近一年使用:0次
名校
解题方法
9 . 如图,在四棱锥
中,
平面
,
,且
,
,
.
(1)求证:
;
(2)求平面
与平面
的夹角;
(3)在线段
上是否存在一点
,使得直线
与平面
垂直,如果垂直,求此时点
到平面
的距离,如果不垂直,说明理由.
![](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/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833cfda415649b832cc136caed392753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cfc9df9c661bd93b3f4f51f91534c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/6/e2a1a7dc-b2b9-435c-adce-66521506289f.png?resizew=158)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecf6c62979a7aa534a191d8387a741e8.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(3)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ddb7c2ca1b6bee86cb24fed02e40da2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
2023-11-14更新
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3卷引用:天津市武清区南蔡村中学2023-2024学年高二上学期第二次月考数学试题
天津市武清区南蔡村中学2023-2024学年高二上学期第二次月考数学试题北京市第五中学2024届高三上学期第二次阶段检测(期中)数学试题(已下线)模块五 全真模拟篇 基础2 期末终极研习室(2023-2024学年第一学期)高三
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解题方法
10 . 直三棱柱
中,
,
,
为
的中点,异面直线
与
所成角的余弦值是______ .
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