1 . 如图,三棱柱
所有的棱长均为1,且四边形
为正方形,又
.
![](https://img.xkw.com/dksih/QBM/2021/1/29/2646607720415232/2646698645954560/STEM/dc550430-4f68-4e48-a5ff-84cb4cf9e4df.png)
(Ⅰ)求证:
;
(Ⅱ)求直线
和平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b387bd1fd555508a3c81162ff36a50f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7870cee007535b979d35bc7feab75616.png)
![](https://img.xkw.com/dksih/QBM/2021/1/29/2646607720415232/2646698645954560/STEM/dc550430-4f68-4e48-a5ff-84cb4cf9e4df.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f389796c8fa08d8f91e9cbb1a08e438.png)
(Ⅱ)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
您最近一年使用:0次
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829次组卷
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5卷引用:浙江省湖州市2020-2021学年高三上学期期末数学试题
浙江省湖州市2020-2021学年高三上学期期末数学试题(已下线)8.5 空间直线、平面的垂直--2020--2021高中数学新教材配套提升训练(人教A版必修第二册)(已下线)8.6空间直线、平面的垂直(2)(精炼)-2020-2021学年高一数学一隅三反系列(人教A版2019必修第二册)湖北省2020-2021学年高二下学期3月联考数学试题浙江省杭州市桐庐分水高级中学2021届高三下学期回头考数学试题
名校
解题方法
2 . 已知四面体
中,二面角
的大小为
,且
,
,
,则四面体
体积的最大值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ec2524be492bca0d1566bf848066f10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e673ef2d48215ca84a48377f17d6df00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd3b76789cbb20517f95286e2add718a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2021-01-29更新
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860次组卷
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7卷引用:浙江省湖州市2020-2021学年高三上学期期末数学试题
浙江省湖州市2020-2021学年高三上学期期末数学试题浙江省温州中学2021届高三下学期2月返校考试数学试题(已下线)专题05 空间几何体的三视图、表面积和体积-备战2021届高考数学(理)二轮复习题型专练?(通用版)(已下线)专题06 空间中的平行与垂直-备战2021届高考数学(理)二轮复习题型专练?(通用版)(已下线)专题06 空间中的平行与垂直-备战2021届高考数学(文)二轮复习题型专练?(通用版)(已下线)技巧01 选择题解法与技巧 第二篇 解题技巧篇(练)-2021年高考数学二轮复习讲练测(浙江专用)浙江省杭州市桐庐分水高级中学2021届高三下学期回头考数学试题
名校
3 . 已知点
是正方体
底面
内一动点,且满足
,设
与平面
所成的角为
,则
的最大值为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/17/c7ba89a2-94f2-4bb6-9fc6-61e9dd7a11c0.png?resizew=175)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce907e681540797c83646f17f2cc9f39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79039b211d151710a15fc9dda11d6225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/17/c7ba89a2-94f2-4bb6-9fc6-61e9dd7a11c0.png?resizew=175)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2021-11-14更新
|
1168次组卷
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6卷引用:浙江省湖州中学2020届高三下学期高考模拟测试(四)数学试题
名校
解题方法
4 . 如图,在长方形
中,
,现将
沿
折至
,使得二面角
为锐二面角,设直线
与直线
所成角的大小为
,直线
与平面
所成角的大小为
,二面角
的大小为
,则
的大小关系是( )
![](https://img.xkw.com/dksih/QBM/2020/12/22/2619899361886208/2620220709052416/STEM/d2f0416f528449bbbc06174854a15e7e.png?resizew=194)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27de5a8c12bfe7c507d9f90b338ed51d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c1335dec9b6a1dcc7b18f7b3989c4cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/117df8d6647d18763502cc18718ccaab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/117df8d6647d18763502cc18718ccaab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f435efcc7869eec21bdba1ed81dc3f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61ba63ad02b1d5af2982fac3d91eb15c.png)
![](https://img.xkw.com/dksih/QBM/2020/12/22/2619899361886208/2620220709052416/STEM/d2f0416f528449bbbc06174854a15e7e.png?resizew=194)
A.![]() | B.![]() | C.![]() | D.不能确定 |
您最近一年使用:0次
2020-12-23更新
|
961次组卷
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9卷引用:浙江省湖州中学2019-2020学年高三下学期3月月考(网测)数学试题
浙江省湖州中学2019-2020学年高三下学期3月月考(网测)数学试题(已下线)专题17 立体几何中的折叠、最值、探索性问题-冲刺2020高考跳出题海之高三数学模拟试题精中选萃(浙江专版)(已下线)【新东方】【2020】【高二上】【期中】【HD-LP362】【数学】(已下线)【新东方】杭州新东方高中数学试卷359浙江省宁波市效实中学2020-2021学年高二上学期期中数学试题(已下线)【新东方】杭州新东方数学试卷409(已下线)专题10 立体几何线面位置关系及空间角的计算 第一篇 热点、难点突破篇(练)-2021年高考数学二轮复习讲练测(浙江专用)(已下线)专题06 立体几何初步(难点)-2020-2021学年高一数学下学期期末专项复习(北师大版2019必修第二册)四川省泸县第一中学2023-2024学年高三上学期10月月考数学(理)试题
名校
解题方法
5 . 如图,三棱柱
中,
底面
,且
为正三角形,
为
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/451ed369-a11b-41df-bf2f-feb355d9e6ff.png?resizew=163)
(1)求证:直线
平面
;
(2)求证:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/451ed369-a11b-41df-bf2f-feb355d9e6ff.png?resizew=163)
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1496afecd92a619fbe5e9b736f06f4e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a935b7d21a103a264b6e96ecf82dbe4a.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f7d9ac3c0e60f1419dc90a37ff731b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
您最近一年使用:0次
2021-08-24更新
|
440次组卷
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9卷引用:【校级联考】浙江省湖州市长兴县、安吉县、德清县2018-2019学年高二(上)期中考试数学试题
【校级联考】浙江省湖州市长兴县、安吉县、德清县2018-2019学年高二(上)期中考试数学试题【全国百强校】广州市第二中学2017-2018学年度高一上数学期末复习题1【全国百强校】广州市第二中学2017-2018学年高一上学期期末复习一数学试题江西省赣州市南康区南康中学2019-2020学年高二上学期10月月考数学试题1湖南省怀化市2019-2020学年高一上学期期末数学试题安徽省亳州市涡阳县第九中学2019-2020学年高二下学期期末数学(文)试题江苏省南京师范大学附属中学江宁分校2020-2021学年高二上学期期初数学试题江西省南昌市豫章中学2021-2022学年高二入学调研(B)数学(文)试题浙江省湖州市长兴县、安吉县、德清县等三县2018-2019学年高二上学期期中数学试题
名校
6 . 已知m,n是两条不同直线,
,
是两个不同平面且
,则下列命题正确的( )
![](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/40b707f5ee4fbb2e637c65fbc6d8ed03.png)
A.若m,n为异面直线且![]() ![]() |
B.若m,n为共面直线且![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() |
您最近一年使用:0次
2020-11-27更新
|
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6卷引用:浙江省湖州市三贤联盟2020-2021学年高二上学期期中联考数学试题
浙江省湖州市三贤联盟2020-2021学年高二上学期期中联考数学试题(已下线)【新东方】【2020】【高二上】【期中】【HD-LP365】【数学】(已下线)【新东方】杭州新东方高中数学试卷363江西省吉安县立中学2020-2021学年高二12月月考数学(理A)试题(已下线)第一章 点线面位置关系 专题二 空间垂直关系的判定与证明 微点2 空间直线垂直的判定与证明综合训练【培优版】(已下线)8.6.2直线与平面垂直(第2课时) 直线与平面垂直的性质(分层作业)-【上好课】
7 . 如图,已知三棱柱
的所有棱长都相等,侧棱
底面
,
分别是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/22/17c49274-0b7c-449e-b85d-30135c078fe9.png?resizew=130)
(1)求证:
;
(2)求平面
与底面
所成二面角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4fb1884afa6b9d2625b489d6a0b4667.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/22/17c49274-0b7c-449e-b85d-30135c078fe9.png?resizew=130)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29d44ef8e93c00b19e79a02424734035.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a03952d664fba91020fc5f3bcf2f9746.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
名校
8 . 如图,已知四棱锥
中,
平面
,
,
,
,
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/24/357b72c2-4d02-4409-ba34-bdcca31b9b71.png?resizew=148)
(Ⅰ)求证:
平面
;
(Ⅱ)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5164a3cc47e266446d49127e2ef10c37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d78fc7fcb2762de28dcef8aa3aa0e49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60bb2e3631f46fc8a24595efce01a92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95a078495ba47076ccaa28b46f765d80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47a6fb3ab9f27db017de6f80074715b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3a6dcaf9f9e9a940b4a16f7ec2fc2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/24/357b72c2-4d02-4409-ba34-bdcca31b9b71.png?resizew=148)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
(Ⅱ)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
您最近一年使用:0次
2020-11-17更新
|
997次组卷
|
4卷引用:浙江省湖州市三贤联盟2020-2021学年高二上学期期中联考数学试题
浙江省湖州市三贤联盟2020-2021学年高二上学期期中联考数学试题(已下线)【新东方】【2020】【高二上】【期中】【HD-LP365】【数学】(已下线)【新东方】杭州新东方高中数学试卷363江西省吉安县立中学2020-2021学年高二12月月考数学(理A)试题
名校
解题方法
9 . 如图,在四棱锥
中,
平面
,底面
是直角梯形,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
,
,
,若动点
在
内及边上运动,使得
,则三棱锥
的体积最大值为______ .
![](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/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c301998d64e8565371dcc4a28debf88b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/491c3a4f72b84ebadd28b90711435adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc24d5628f9d905969dfc323caab303d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7edc2e23df190c35aafad93410a05b8a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/25/ca2a26c2-9357-4142-b01a-3924931f61b9.png?resizew=175)
您最近一年使用:0次
2020-11-17更新
|
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8卷引用:浙江省湖州市三贤联盟2020-2021学年高二上学期期中联考数学试题
浙江省湖州市三贤联盟2020-2021学年高二上学期期中联考数学试题(已下线)【新东方】【2020】【高二上】【期中】【HD-LP365】【数学】(已下线)【新东方】杭州新东方高中数学试卷363广东省、辽宁省、湖北省、湖南省、重庆市等八省市2021届高三(上)适应性数学试题八省市2021届高三新高考统一适应性考试江苏省无锡市天一中学考前热身模拟数学试题江苏省南京市中华中学2020-2021学年高二上学期期末数学试题(已下线)考点41 点、直线、平面之间的位置关系-备战2021年高考数学经典小题考前必刷(新高考地区专用)江苏省常州市第一中学2021-2022学年高二下学期4月月考数学试题
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10 . 如图,四棱锥
中,底面为直角梯形,
,
,
,
.在锐角
中,
是边
上一点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/107d5131-8738-45fe-87d9-0ed52ed0f7a1.jpg?resizew=168)
(1)求证:
平面
;
(2)若
与平面
所成角的正弦值是
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce0d7095ddd69d6ceaf1065b1bc2c79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d774e0a056deb1f08fc1a2dee19207c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b44f4120c94cb7176dc31fcac387b32e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.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/28f55c2a6a1cac9434acdf5a56f034ef.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/107d5131-8738-45fe-87d9-0ed52ed0f7a1.jpg?resizew=168)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa69a2247ad4d5231aa361349b12f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
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