名校
1 . 如图,在四棱锥
中,底面
为菱形,
平面
,
为
的中点.
与直线
相交于点
,求证:
;
(2)若
,
,
,求直线
与平面
所成角的大小.
![](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/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bd8a97f37156cec6592795da3941f87.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4f5eec0addba78f2e0cdfb7ecc59a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad069cd8a8fd2f00a1bb8f60c9a73241.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
您最近一年使用:0次
2024-04-20更新
|
2943次组卷
|
3卷引用:上海市松江区2024届高三下学期模拟考质量监控(二模)数学试卷
上海市松江区2024届高三下学期模拟考质量监控(二模)数学试卷河南省封丘县第一中学2023-2024学年高一下学期第二次阶段性测数学试题(已下线)专题03空间向量及其应用--高二期末考点大串讲(沪教版2020选修)
名校
2 . 三棱柱
中,
,线段
的中点为
,且
.
平面
;
(2)求平面
与平面
所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c4ea6e75dc186c199368d0e54af3247.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/736eca86008d535f03500d32ac00cd46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0edb1508fc95765f3bb316bcb5252d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3b3ee1980ad0962ffc43803148ebe83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85f6a1b0761cb375279e1b76e6c2eefc.png)
您最近一年使用:0次
2024-01-15更新
|
444次组卷
|
4卷引用:上海市松江区华东政法大学附属松江高级中学2023-2024学年高二下学期3月月考数学试题
上海市松江区华东政法大学附属松江高级中学2023-2024学年高二下学期3月月考数学试题上海市闵行区七宝中学2024届高三上学期期末数学试题(已下线)2024年高考数学二轮复习测试卷(上海专用)(已下线)专题07 空间向量与立体几何(九大题型+优选提升题)-【好题汇编】备战2023-2024学年高二数学下学期期末真题分类汇编(沪教版2020选择性必修,上海专用)
2024·全国·模拟预测
名校
解题方法
3 . 如图,四棱锥
中,底面
是平行四边形,
平面
,点
是
的中点,
分别是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/8/4ffa1eea-e765-4416-96b0-aca02b50c04e.png?resizew=166)
(1)求证:
;
(2)求三棱锥
的体积.
![](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/3c893f51345fa193c688f4ce4fffdfe0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa834ab3fc4111e0c39c67b7b1541d96.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/8/4ffa1eea-e765-4416-96b0-aca02b50c04e.png?resizew=166)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7a772e2dea744532fd06fa33701fac3.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a54111e491768afe053bbb665a17a90c.png)
您最近一年使用:0次
4 . 如图,在四棱锥
中,
底面
,
,点
在线段
上,且
.
![](https://img.xkw.com/dksih/QBM/2023/12/6/3383499625168896/3383520292151296/STEM/9a7906d55486403d8f566d19f0615bcf.png?resizew=186)
(1)求证:
平面
;
(2)若四棱锥
的体积为
,
,
,
,
,求二面角
的大小.
![](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/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a763381e4a9e6ac9d9c1df51122570f8.png)
![](https://img.xkw.com/dksih/QBM/2023/12/6/3383499625168896/3383520292151296/STEM/9a7906d55486403d8f566d19f0615bcf.png?resizew=186)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44b190c8d3d7d7d0e6e959e8a52eae90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)若四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c6c7567972273b4ba733b47bf9d5408.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d79e7020414add95907e061df505ef0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/375593174c13ec0b8e6200fab322d9b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5ba4ee1fd8cf910368d77571a9289b7.png)
您最近一年使用:0次
名校
解题方法
5 . 已知平面
内的角
,线段
是平面
的斜线段且
,
,那么点
到平面
的距离是_______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14b5d523373b8cbfa33e42a1bf154544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17e6544b03ad07d547669ae15089c487.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f838d37fdeae11ef8f9cef750b7c6469.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
您最近一年使用:0次
6 . 已知
,
是异面直线,
,
是两个不同的平面,且
,
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/539a38ada26356d73024fb8533449c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/209323a7a4d015f7e570ec578c1731f7.png)
A.若![]() ![]() | B.若![]() ![]() |
C.若![]() ![]() | D.若![]() ![]() |
您最近一年使用:0次
2023-09-05更新
|
374次组卷
|
3卷引用:上海市松江二中2023-2024学年高二上学期10月月考数学试题
名校
解题方法
7 . 如图:
平面
,四边形
为直角梯形,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8813d2841a6515e9ffaea16c6011cdeb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/24/e5cc76df-dd11-4d16-8049-1a92156550c7.png?resizew=163)
(1)求证:平面
平面
;
(2)求二面角
的余弦值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.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/20148dfbb5c2c03ed5387e7d2ce04b96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8813d2841a6515e9ffaea16c6011cdeb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/24/e5cc76df-dd11-4d16-8049-1a92156550c7.png?resizew=163)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36824d6beda179820ac115d1258e8a8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1069d514c3c32aeabd274475ee209ed6.png)
您最近一年使用:0次
2023-03-21更新
|
414次组卷
|
2卷引用:上海市松江一中2023届高三下学期3月月考数学试题
名校
解题方法
8 . 已知正方体
,点
,
,
分别是线段
,
和
上的动点,观察直线
与
,
与
给出下列结论:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/1/c6dd710e-3db8-48fd-89a2-2e0f09bdc82a.png?resizew=143)
①对于任意给定的点
,存在点
,使得
;
②对于任意给定的点
,存在点
,使得
;
③对于任意给定的点
,存在点
,使得
;
④对于任意给定的点
,存在点
,使得
.
其中正确的结论是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1859959fdb4c5edd8056893f94a10a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d41164f8a9f6fe32a9364f18f168dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab56db50d7ace3d6ead190be9432e5ac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/1/c6dd710e-3db8-48fd-89a2-2e0f09bdc82a.png?resizew=143)
①对于任意给定的点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ded0c7bfe29be3c9757e20df65dd93.png)
②对于任意给定的点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d883886686e00e1e7a59998f1b0b610c.png)
③对于任意给定的点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/155d398cf0cdabae814b03785b2d5ea4.png)
④对于任意给定的点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4c8dc844e3a59c700067cef359bf6b8.png)
其中正确的结论是( )
A.① | B.②③ | C.①④ | D.②④ |
您最近一年使用:0次
2023-01-29更新
|
637次组卷
|
10卷引用:上海市松江二中2023-2024学年高二上学期10月月考数学试题
上海市松江二中2023-2024学年高二上学期10月月考数学试题2014-2015学年重庆市第七中学高二上学期期末考试理科数学试卷上海市西南位育中学2020-2021学年高二下学期期中数学试题(已下线)2021年新高考浙江数学高考真题变式题6-10题(已下线)数学(乙卷文科)北京市人大附中2022届高三上学期数学收官考试之期末模拟试题上海市嘉定区第一中学2021-2022学年高二上学期12月月考数学试题重庆市缙云教育联盟2022-2023学年高一下学期期末数学试题(已下线)期中真题必刷压轴50题专练-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(沪教版2020必修第三册)(已下线)第10章 空间直线与平面(压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020必修第三册)
名校
解题方法
9 . 如图,在圆柱
中,
是圆柱的母线,
是圆柱的底面
的直径,
是底面圆周上异于
、
的点.
平面
;
(2)若
,
,
,求圆柱
的侧面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/714cc3707bba3bfdb56e251999be8592.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e673ef2d48215ca84a48377f17d6df00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1682d306c38087d9e6f7efb9cec596a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
您最近一年使用:0次
2023-01-29更新
|
4463次组卷
|
21卷引用:上海外国语大学西外外国语学校2021-2022学年高二上学期期中数学试题
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名校
10 . 如图,已知四面体
中,
平面
,
.
![](https://img.xkw.com/dksih/QBM/2023/1/11/3150440558288896/3150756208951296/STEM/341340cd0e2846c889c35ee695ee889d.png?resizew=181)
(1)求证:
;
(2)《九章算术》中将四个面都是直角三角形的四面体称为“鳖臑”,若此“鳖臑”中,
,有一根彩带经过面
与面
,且彩带的两个端点分别固定在点
和点
处,求彩带的最小长度;
(3)若在此四面体中任取两条棱,记它们互相垂直的概率为
;任取两个面,记它们互相垂直的概率为
;任取一个面和不在此面上的一条棱,记它们互相垂直的概率为
. 试比较概率
、
、
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd6a2b112facda441f4e34bf5c145fa.png)
![](https://img.xkw.com/dksih/QBM/2023/1/11/3150440558288896/3150756208951296/STEM/341340cd0e2846c889c35ee695ee889d.png?resizew=181)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bf10d92f20501e19d25f6f4159aab89.png)
(2)《九章算术》中将四个面都是直角三角形的四面体称为“鳖臑”,若此“鳖臑”中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce519312a849963b376c202c3f9d7cf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(3)若在此四面体中任取两条棱,记它们互相垂直的概率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
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