名校
1 . 如图,正方体的棱长为3,E为AB的中点,
,动点M在侧面
内运动(含边界),则( )
A.若![]() ![]() ![]() |
B.平面![]() ![]() |
C.平面![]() ![]() ![]() |
D.不存在一条直线l,使得l与正方体![]() |
您最近一年使用:0次
2023-05-06更新
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1769次组卷
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4卷引用:湖南省长沙市雅礼中学2023届高三一模数学试题
湖南省长沙市雅礼中学2023届高三一模数学试题吉林省普通高中友好学校第三十六届联合体2022-2023学年高一下学期期中联考数学试题(已下线)模块三 专题3 小题满分挑战练(1)(人教B)(已下线)第三章 空间轨迹问题 专题一 立体几何轨迹常见结论及常见解法 微点1 立体几何轨迹常见结论及常见解法(一)【培优版】
2 . 如图,已知斜四棱柱
,底面
为等腰梯形,
,点
在底面
的射影为
,且
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/9/6322f190-0547-4fa4-8bac-06ca219903c3.png?resizew=260)
(1)求证:平面
平面
;
(2)若
为线段
上一点,且平面
与平面
夹角的余弦值为
,求直线
与平面
所成角的正弦值.
![](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/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c1c788096ba7560ceb6db87763e88ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6f546825da254e8378dc074cc2c8562.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc0a886f1192d450ced9fd875e78425e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/9/6322f190-0547-4fa4-8bac-06ca219903c3.png?resizew=260)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2730b513bd3359c3dfe6567e04f5ef9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3aace91caec728e174daec29a3568ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9399c9a2a31b0e3165aea2d6ccc4f7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2730b513bd3359c3dfe6567e04f5ef9.png)
您最近一年使用:0次
2023-04-07更新
|
1633次组卷
|
2卷引用:湖南省长沙市长郡中学2024届高三上学期期末适应性考数学试题
名校
解题方法
3 . 如图,在三棱锥P-ABC中,∠ACB=90°,PA⊥底面ABC.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/1/9757cabc-de2f-4346-95e8-552c89440e03.png?resizew=163)
(1)求证:平面PAC⊥平面PBC;
(2)若AC=BC=PA,求平面PAB与平面PCB所成二面角的大小.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/1/9757cabc-de2f-4346-95e8-552c89440e03.png?resizew=163)
(1)求证:平面PAC⊥平面PBC;
(2)若AC=BC=PA,求平面PAB与平面PCB所成二面角的大小.
您最近一年使用:0次
2023-03-31更新
|
696次组卷
|
5卷引用:湖南省长沙市芙蓉高级中学2022-2023学年高二上学期期中数学试题
名校
4 . 在如图所示试验装置中,两个长方形框架
与
全等,
,
,且它们所在的平面互相垂直,活动弹子
分别在长方形对角线
与
上移动,且
,则下列说法正确的是( )
![](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/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ab4007a35a23105744177d982caf747.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6af56667f167c0b25fbfbfd619363e9.png)
A.![]() |
B.![]() ![]() |
C.当![]() ![]() ![]() ![]() |
D.![]() |
您最近一年使用:0次
2023-03-03更新
|
926次组卷
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3卷引用:湖南省长沙市雅礼中学2023届高三下学期月考(七)数学试题
名校
5 . 如图,已知圆锥
,AB是底面圆О的直径,且长为4,C是圆O上异于A,B的一点,
.设二面角
与二面角
的大小分别为
与
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/1/c98fcac6-5de2-4237-83ea-e8653b1e73e1.png?resizew=201)
(1)求
的值;
(2)若
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/967f74b8993c61634ceed95edca05ffd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf29d07c3751c41ab3503065a5a5052e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b796bbaeb8450404c2d146283562006e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/1/c98fcac6-5de2-4237-83ea-e8653b1e73e1.png?resizew=201)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5458c30dbb22889ed27b78ae92f89e78.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf76792693c3d26302f7631276f14398.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a438393ddfc7da1804baf4932442bb35.png)
您最近一年使用:0次
2023-02-24更新
|
1843次组卷
|
9卷引用:湖南省衡阳市第八中学2023届高三高考适应性考试数学试题
湖南省衡阳市第八中学2023届高三高考适应性考试数学试题江苏省新高考基地学校2021届高三下学期4月第二次大联考数学试题(已下线)2021年秋季高三数学开学摸底考试卷03(江苏专用)陕西省汉中市某校2022-2023学年高三上学期第三次质量检测理科数学试题山东省日照市2023届高三一模考试数学试题河南省安阳一中、鹤壁高中、新乡一中2023届高三下学期联考理科数学试题(已下线)山东省日照市2023届高三一模考试数学试题变式题17-22江苏省连云港市灌南高级中学2023届高三下学期3月解题能力竞赛数学试题重庆市七校2023届高三三诊数学试题
解题方法
6 . 如图所示,
平面
,
,
,
,则二面角
的余弦值大小为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb4f142d753f5878ad14a8623d46cb46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f144992e1cbee34868abce1e5ad38c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a438393ddfc7da1804baf4932442bb35.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/15/48477781-dfc7-460a-9ce6-693d090fa6ee.png?resizew=140)
您最近一年使用:0次
名校
解题方法
7 . 如图,在直四棱柱
中,底面
是梯形,且
,E是棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/9/ef09a21b-9cfc-4f5e-8433-b8d757f7ba1e.png?resizew=223)
(1)求证:
;
(2)求点
到平面
的距离;
(3)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29796da2cfd31deeb592b0f5a4ab9f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/9/ef09a21b-9cfc-4f5e-8433-b8d757f7ba1e.png?resizew=223)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4ab7e657f01bdfa235f8c4d6681d13.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f7989987e76fe40de8b7533a22912a2.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e14626adb4b79a83e54365ff76c75e52.png)
您最近一年使用:0次
8 . 如图,在四棱锥
中,已知
,
,
,
,
,
,
为
中点,
为
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/9/e19792f1-39e4-4b38-be6d-34a1504853c3.png?resizew=196)
(1)证明:平面
平面
;
(2)若
,求平面
与平面
所成夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21b69c41147a67cb486426ee88bd41ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22661c00094a4625b2e68b4e4ea676ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b60f7441172407b19e9e61b85a0170d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d82e3d915a1eef13aad9147610c7db2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6610676353016a9f7235d306b731c1e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42789f54f6d3e1d508837711c6a873b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.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/2023/2/9/e19792f1-39e4-4b38-be6d-34a1504853c3.png?resizew=196)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60b9658dd92f4bc8ec3d68534e48e16a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b6aeaf411b82c8a3b2770ac1262cc62.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd3eb538f36e6e722e4ce125266b99b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30f457418e6a7e21f0ed0bf490a3709c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
您最近一年使用:0次
2023-02-04更新
|
3946次组卷
|
5卷引用:湖南师范大学附属中学2023届高三下学期月考(七)数学试题
湖南师范大学附属中学2023届高三下学期月考(七)数学试题浙江省Z20名校联盟(浙江省名校新高考研究联盟)2023届高三第二次联考数学试题(已下线)专题2 求二面角的夹角(1)广东省佛山市第一中学2023届高三4月一模数学试题(已下线)立体几何专题:空间二面角的5种求法
9 . 如图所示的正方体
中,点
分别是棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/16/a3d43ffb-141d-43ba-a1c2-7d5c9bb64112.png?resizew=128)
(1)证明:平面
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/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f44765186186e1effac383c9833b070c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/16/a3d43ffb-141d-43ba-a1c2-7d5c9bb64112.png?resizew=128)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4a46fbde58e12b1edc038ae9e921722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2bf9ef324f1289e205e29fed105c38e.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
您最近一年使用:0次
名校
解题方法
10 . 截角四面体是一种半正八面体,可由四面体经过适当的截角,即截去四面体的四个顶点所产生的多面体.如图所示,将棱长为
的正四面体沿棱的三等分点作平行于底面的截面,得到所有棱长均为a的截角四面体,则下列说法错误的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/c9279c45-53e4-4fde-8e18-d1c8022ffd15.png?resizew=165)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9878a063abcb6098d10560f2bf2d4b71.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/c9279c45-53e4-4fde-8e18-d1c8022ffd15.png?resizew=165)
A.二面角![]() ![]() |
B.该截角四面体的体积为![]() |
C.该截角四面体的外接球表面积为![]() |
D.该截角四面体的表面积为![]() |
您最近一年使用:0次
2023-01-12更新
|
1396次组卷
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6卷引用:湖南省邵阳市2023届高三上学期一模数学试题
湖南省邵阳市2023届高三上学期一模数学试题湖南省长沙市宁乡市第一高级中学2022-2023学年高三上学期12月月考数学试题重庆市第八中学校2022届高三下学期调研检测(十四)数学试题(已下线)模块五 空间向量与立体几何-2(已下线)专题2 求二面角的夹角(2)专题15空间向量与立体几何(选填题)(2)