名校
解题方法
1 . 如图,
,
分别是直径
的半圆
上的点,且满足
,
为等边三角形,且与半圆
所成二面角的大小为
,
为
的中点.
平面
;
(2)在弧
上是否存在一点
,使得直线
与平面
所成角的正弦值为
?若存在,求出点
到平面
的距离;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e925392d0bf25a1a5c698ec1d8adea4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)在弧
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ab8a10e675354fa0c6e7da3d06b999d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93919b1b42b96052bb1ef51d2c6e90c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ab8a10e675354fa0c6e7da3d06b999d.png)
您最近一年使用:0次
2024-03-20更新
|
670次组卷
|
4卷引用:广西百色市平果市铝城中学2023-2024学年高二下学期4月月考测试数学试卷
2 . 已知正方体
的棱长为2,点
是
的中点,点
满足
,
,则下列结论正确的是( )
![](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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8ee2271ff6f44f9a0bd27c3d5cd704e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eb6bf23a5a12e1ba5413594d7b1a57c.png)
A.![]() ![]() | B.![]() ![]() ![]() |
C.![]() ![]() | D.三棱锥![]() ![]() |
您最近一年使用:0次
名校
3 . 在如图所示的五面体
中,
共面,
是正三角形,四边形
为菱形,
平面
,点
为
中点.
(1)证明:
平面
;
(2)已知
,求平面
与平面
所成二面角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/441dec590b47adc3678a291a3ec89a4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1fb8cb34faf00dad5c219228c4afa8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cfa0043704a0996ceb7483787957b3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/1824ac5d-7573-4c80-b479-d80299739305.png?resizew=192)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60e39231557268a8cf695d2b55b6569f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae8768996ca9a0f2c5d9a19abbd54df.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b32e96ff696a5c9d84fd5ab6cefd67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae8768996ca9a0f2c5d9a19abbd54df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a814b70236a108be5d6e7ff271fe92.png)
您最近一年使用:0次
2024-02-24更新
|
2098次组卷
|
4卷引用:广西壮族自治区南宁市第三中学、柳州高级中学2024届高三下学期一轮复习诊断性联考数学试卷
4 . 如图,在棱长为2的正方体
中,
分别是棱
的中点,则下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/c99e7102-f228-4d7e-831f-8a1c456ca588.png?resizew=159)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7db31b6ce9408706f77680ac8c75c2ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b318a89e8653ef62c66bae95ac1ab10.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/c99e7102-f228-4d7e-831f-8a1c456ca588.png?resizew=159)
A.![]() ![]() |
B.![]() ![]() ![]() |
C.异面直线![]() ![]() |
D.平面![]() ![]() |
您最近一年使用:0次
2024-02-20更新
|
829次组卷
|
3卷引用:广西壮族自治区2023-2024学年高二下学期3月联考数学试卷
解题方法
5 . 如图,在正方体
中,
为平面
的中心.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/13/1ee695fe-0aca-4c2d-8ef3-c50b6aed425f.png?resizew=159)
(1)求证:
平面
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bafa7168302e524813426a0fa494c86f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/13/1ee695fe-0aca-4c2d-8ef3-c50b6aed425f.png?resizew=159)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34d28074ee5af1441242700388b3a9c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a935b7d21a103a264b6e96ecf82dbe4a.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a935b7d21a103a264b6e96ecf82dbe4a.png)
您最近一年使用:0次
6 . 如图,在直角梯形
中,
,
,
.以直线
为轴,将直角梯形
旋转得到直角梯形
,且
.
(1)求证:
平面
;
(2)在线段
上是否存在点
,使得直线
和平面
所成角的正弦值为
?若存在,求出
的值;若不存在,说明理由.
![](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/b2b377f22aafd3742ad860f77abaacef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/555e29e445c95ddb514840f63fbb1d12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f345b28a81ff3d2c4666ee945a426fa9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/30/b13e83fc-b04b-466b-b888-6f30f190713b.png?resizew=208)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40f44f2b2f82a9126223138972850aa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1b489c25405ce48699d4f0a62820bed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a21bec66ceb1f04350a01ba851d8495.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc8f45af58d68d63aeebf7ea8ecfac4.png)
您最近一年使用:0次
名校
解题方法
7 . 如图,在正方体
中,
为
的中点.
平面
;
(2)
上是否存在一点
,使得平面
平面
,若存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f11f1840eb8b17e7b07c3fe7e987a9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f88a05162ce6fae872f415e4581b83ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3c241f900cb6ed341c137a3d71216a4.png)
您最近一年使用:0次
2024-03-16更新
|
4575次组卷
|
28卷引用:广西壮族自治区河池市十校联体2023-2024学年高一下学期第二次联考(5月)数学试题
广西壮族自治区河池市十校联体2023-2024学年高一下学期第二次联考(5月)数学试题广西百色市2022-2023学年高一下学期数学期末考试模拟试题(已下线)考点巩固卷17 空间中的平行与垂直(八大考点)(已下线)专题6-3立体几何大题综合归类-2(已下线)13.2.4 平面与平面的位置关系(1)-【帮课堂】(苏教版2019必修第二册)(已下线)高一下学期期中复习解答题压轴题十八大题型专练(2)-举一反三系列(人教A版2019必修第二册)河南省新乡市封丘县第一中学2023-2024学年高一下学期期中数学试题(已下线)专题19 平面与平面平行-《重难点题型·高分突破》(人教A版2019必修第二册)(已下线)8.5空间直线、平面的平行——随堂检测(已下线)专题05 空间直线﹑平面的平行-《知识解读·题型专练》(人教A版2019必修第二册)(已下线)8.5.3 平面与平面平行-同步题型分类归纳讲与练(人教A版2019必修第二册)广东省汕头市潮阳实验学校2023-2024学年高一下学期期中考试数学试题四川省攀枝花市第三高级中学2023-2024高一下学期第二次月考数学试题(已下线)6.4.2平面与平面平行-【帮课堂】(北师大版2019必修第二册)(已下线)专题突破:空间几何体的动点探究问题-同步题型分类归纳讲与练(人教A版2019必修第二册)(已下线)核心考点5 立体几何中的位置关系 B提升卷 (高一期末考试必考的10大核心考点)湖南省长沙市第二十一中学2021-2022学年高一上学期期中数学试题山西省大同市第二中学校2021-2022学年高一下学期期中数学试题河南省商丘市宁陵县高级中学2021-2022学年高一下学期第二次月考数学试卷(B)(已下线)第47讲 直线与平面、平面与平面平行(已下线)8.5.3 平面与平面平行 (精讲)(1)-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)(已下线)8.5.3 平面与平面平行(精讲)-【题型分类归纳】2022-2023学年高一数学同步讲与练(人教A版2019必修第二册)专题6.3 空间中的平行关系-2021-2022学年高一数学北师大版2019必修第二册陕西省西安市西北工业大学附属中学2022-2023学年高一下学期期中数学试题(已下线)第03讲 空间中平行、垂直问题10种常见考法归类(1)(已下线)第03讲 空间中平行、垂直问题10种常见考法归类(2)(已下线)10.4 平面与平面间的位置关系(第1课时)(七大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020必修第三册)甘肃省兰州市兰州新区兰州新区高级中学2022-2023学年高一下学期期末数学试题
名校
解题方法
8 . 长方体
中,
,底面
是边长为
的正方形,底面
中心为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d927585a17c2e98ef7d5a9589a26ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
A.![]() ![]() |
B.向量![]() ![]() ![]() |
C.四棱锥![]() ![]() |
D.直线![]() ![]() ![]() |
您最近一年使用:0次
2023-01-15更新
|
882次组卷
|
6卷引用:广西壮族自治区百色市平果市铝城中学2023-2024学年高二下学期开学考试数学试卷
名校
9 . 四棱锥
底面为平行四边形,且
,
,
,
平面
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/15/47ea1ba2-dc87-4d5a-928e-1e5ba34932aa.png?resizew=232)
(1)点
在棱
上,且
,求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
平面
;
(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/2022/10/15/47ea1ba2-dc87-4d5a-928e-1e5ba34932aa.png?resizew=232)
(1)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ec34fb844a3a9989e1cbf930f138ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1885efcff0b903e314057dd153578600.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
2022-10-13更新
|
503次组卷
|
4卷引用:广西壮族自治区百色市平果市铝城中学2023-2024学年高二下学期开学考试数学预测试题
名校
10 . 如图,正方体
的棱长为2,E是棱
的中点,F是侧面
上的动点,且满足
平面
,则下列结论中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82b724168afaee2ecddf97257180be18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ea211a573491409cb60f9fbe9a65cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923189afc198d153c79059a827f63c87.png)
A.平面![]() ![]() ![]() |
B.点F的轨迹长度为![]() |
C.存在点F,使得![]() |
D.平面![]() ![]() ![]() |
您最近一年使用:0次
2022-05-28更新
|
2290次组卷
|
10卷引用:广西南宁市第二中学2023-2024学年高二下学期期中考试数学试卷
广西南宁市第二中学2023-2024学年高二下学期期中考试数学试卷广西南宁市第二中学2022-2023学年高一下学期期末考试数学试题广东省广州市黄埔区广州科学城中学2023-2024学年高一下学期5月月考数学试题三湘名校教育联盟2021-2022学年高一下学期5月联考数学试题重庆外国语学校(即四川外国语大学附属外国语学校)2021-2022学年高一下学期6月月考数学试题(已下线)江苏省扬州市2021-2022学年高一下学期期末适应性测试数学试题(已下线)专题22 立体几何中的轨迹问题-1(已下线)高一下期末模拟测试卷二-【单元测试】(苏教版2019必修第二册)河南省濮阳市华龙区第一高级中学2022-2023学年高一下学期6月月考数学试题河南省郑州市郑州中学2022-2023学年高一下学期联考模拟数学试题(三)