1 . 如图,已知
和
都是直角梯形,
,
,
,
,
,
,二面角
的平面角为
.设M,N分别为
的中点.
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68d31600cba2d5256c7e78b6122d6755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c26dbbd583ee4edd5a0fd537ce9e861d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f08273d339dc5ddbb89aa67bb8205e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40560ea08d6cd8c1d4d9661ee6faaa3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4901a7eda97d6a307db76c4fb196ba3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/502807a17f318c77921e75039fead278.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61bfc65bfbc357d43069e9aad18f8625.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34f892d82e656fd14e4464c0f04730d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bdadcc147a7e441decf7561c9e7310e.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
您最近一年使用:0次
2022-06-10更新
|
20929次组卷
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32卷引用:青海省西宁市海湖中学2022-2023学年高二下学期开学摸底考试数学试卷 A卷
青海省西宁市海湖中学2022-2023学年高二下学期开学摸底考试数学试卷 A卷重庆市万州第二高级中学2022-2023学年高二上学期开学考试数学试题湖南省衡阳市衡阳县第四中学2022-2023学年高二平行班下学期开学模拟考试数学试题河南省洛阳市第八高级中学2023届高三下学期开学摸底考试理科数学试题江苏省南京市田家炳高级中学2022-2023学年高二下学期期初考试数学试题2022年新高考浙江数学高考真题(已下线)2022年高考浙江数学高考真题变式题10-12题重庆市第八中学校2021-2022学年高二下学期期末复习数学试题(已下线)专题40:空间角的向量求法-2023届高考数学一轮复习精讲精练(新高考专用)(已下线)第06讲 向量法求空间角(含探索性问题) (讲)-3(已下线)2022年高考浙江数学高考真题变式题19-22题(已下线)第04讲 空间向量在立体几何中的应用(练,理科专用)湖北省武汉市第一中学2022-2023学年高三上学期10月月考数学试题(已下线)模拟卷05湖南省永州市江华瑶族自治县第一中学2022-2023学年高三上学期12月月考数学试题(已下线)专题08 立体几何解答题常考全归类(精讲精练)-1江苏省扬州市仪征中学、江都中学2022-2023学年高三上学期期末阶段联考数学试题湖南省湘潭市湘潭县第一中学2022-2023学年高二下学期3月月考数学试题(已下线)专题八 立体几何-2(已下线)重组卷02(已下线)第4讲 空间向量的应用 (2)(已下线)专题19 空间几何解答题(理科)-3第一章 空间向量与立体几何 (单元测)(已下线)第07讲 空间向量的应用 (2)(已下线)第11讲 用空间向量研究距离、夹角问题11种常见考法归类-【暑假自学课】2023年新高二数学暑假精品课(人教A版2019选择性必修第一册)河南省许昌市禹州市高级中学2023-2024学年高三上学期11月月考数学试题(已下线)第05讲 空间向量及其应用(练习)(已下线)考点12 空间角 2024届高考数学考点总动员 【讲】(已下线)通关练05 空间向量与立体几何近五年高考真题4考点精练(30题)- 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教A版2019选择性必修第一册)浙江省宁波市鄞州中学2023-2024学年高二上学期期中考试数学试题(已下线)模块一 专题6《 空间向量应用》 B提升卷 (苏教版)(已下线)专题23 立体几何解答题(理科)-1
解题方法
2 . 如图,在三棱柱
中,
为边长为
的正三角形,
为
的中点,
,且
,平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/22/dcd0f718-5735-4e7a-b235-9a8883df44aa.png?resizew=195)
(1)证明:
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be445f94888b34161b6d59d458928e35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50d9bdbbdfabc737323692c796e41930.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/22/dcd0f718-5735-4e7a-b235-9a8883df44aa.png?resizew=195)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/005c110169a6aa55414175b8e76fc9da.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed27ea773e11865b0dd40c54822a7e26.png)
您最近一年使用:0次
2023-02-19更新
|
1089次组卷
|
5卷引用:青海省西宁市大通回族土族自治县2022-2023学年高三下学期开学摸底考试数学(文)试题
青海省西宁市大通回族土族自治县2022-2023学年高三下学期开学摸底考试数学(文)试题(已下线)第八章立体几何初步(综合检测卷)(已下线)8.6.3 平面与平面垂直(分层作业)-【上好课】2022-2023学年高一数学同步备课系列(人教A版2019必修第二册)(已下线)8.6.3 平面与平面垂直(1)-2022-2023学年高一数学《考点·题型·技巧》精讲与精练高分突破系列(人教A版2019必修第二册)(已下线)专题8.13 空间直线、平面的垂直(二)(重难点题型精讲)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)
名校
3 . 如图,在四棱锥
中,平面
底面
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/27/73513c62-b690-4ea7-bbbc-43d8ed238583.png?resizew=157)
(1)证明:
.
(2)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/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c2d817d2506f0f2e4a9926f9ba761cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d5fdc99dd2f51a7298c212745b7efc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/27/73513c62-b690-4ea7-bbbc-43d8ed238583.png?resizew=157)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdfa54114f04a75b8c96165b3718ed7f.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2023-02-14更新
|
1039次组卷
|
5卷引用:青海省西宁市六校联考2022-2023学年高三下学期开学考试数学(理)试题
名校
4 . 如图,在四棱锥
中,底面
为梯形,
,
为等边三角形.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/14/6c68634f-6e84-456c-9599-1beec920c305.png?resizew=156)
(1)证明:
平面
.
(2)若
为等边三角形,求平面
与平面
夹角的余弦值.
![](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/b2201efd8a9dfdcd493019090640c3e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88b6c15b3cffca7663acb8197770091c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/14/6c68634f-6e84-456c-9599-1beec920c305.png?resizew=156)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
您最近一年使用:0次
2024-03-14更新
|
750次组卷
|
4卷引用:青海省海南州贵德高级中学2024届高三七模(开学考试)数学(理科)试题
名校
5 . 如图,在三棱柱
中,
为边长为2的正三角形,D为
的中点,
,且
,平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/40bc791f-a3fd-4e66-a33e-e53aee3c4b57.png?resizew=181)
(1)证明:
;
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/719de37e2bbf07a97de22f3353fabac1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50d9bdbbdfabc737323692c796e41930.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/40bc791f-a3fd-4e66-a33e-e53aee3c4b57.png?resizew=181)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/005c110169a6aa55414175b8e76fc9da.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46340bfad3505ef24f4916a61dd1a5e.png)
您最近一年使用:0次
2023-02-19更新
|
363次组卷
|
3卷引用:青海省西宁市大通回族土族自治县2022-2023学年高三下学期开学摸底考试数学(理)试题
名校
6 . 如图,在四棱锥
中,
平面
,四边形
为菱形,
为棱
上一点.
为棱
的中点,平面
平面
,求证:
;
(2)若
,求直线
与平面
所成角的正弦值.
![](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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c659d2ab07b9b66ed9a60cb604dd9aa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48abba67b697688749cf92b8c7205161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9915bc06e82813cec0d8854bb28ac2f9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57dbd79f684c0cc68e1f9becc3f3591b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
您最近一年使用:0次
2023-07-08更新
|
233次组卷
|
2卷引用:青海省海东市第二中学2023-2024学年高二上学期入学考试数学试题
名校
7 . 如图,在棱长为1的正方体
中,点
是线段
上的一点,则下列说法正确的是( )
![](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/e539f26ed5e0b20ff7220559324869a4.png)
A.直线![]() ![]() |
B.![]() ![]() |
C.三棱锥![]() |
D.直线![]() ![]() |
您最近一年使用:0次
2023-07-21更新
|
203次组卷
|
2卷引用:青海省海东市第二中学2023-2024学年高二上学期入学考试数学试题
解题方法
8 . 如图,四棱锥
的底面为直角梯形,
,
,
底面ABCD,且
,M是PB的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/686eb7d7-52e3-4884-a901-c08df6f40414.png?resizew=153)
(1)证明:
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4795ee1f96b430529934e2231b38885d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/586c2a453db84ec5f8a590fafe6e85f4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/686eb7d7-52e3-4884-a901-c08df6f40414.png?resizew=153)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37002ada5d194d4d062fa3285d7d9824.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01897779b865498122b66457e92f2266.png)
您最近一年使用:0次
2022-12-09更新
|
192次组卷
|
2卷引用:青海省西宁市六校联考2022-2023学年高三下学期开学考试数学(文)试题
名校
9 . 如图,在正四棱柱
中,
,
,点
,
分别为
,
的中点,则二面角
的大小为______ ;三棱锥
的外接球的表面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6db57eca2a7cbd91bc57372592580a76.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e7be2f695260a14809dec7d84dfd6fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/580be22c91b2343e7933f8b1d925fc52.png)
您最近一年使用:0次