名校
解题方法
1 . 设
为某正方体的一条体对角线,
为该正方体的各顶点与各棱中点所构成的点集,若从
中任选两点连成线段,则与
垂直的线段数目是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
A.12 | B.21 | C.27 | D.33 |
您最近一年使用:0次
2024-05-31更新
|
356次组卷
|
3卷引用:重庆市重庆乌江新高考协作体2024届高三下学期模拟监测(三)数学试题
名校
解题方法
2 . 如图,已知正方体
的棱长为1,若点E、F是正方形
内(包括边界)的动点,若
,
,则下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/8/3801d1a4-c7a6-4c1b-aceb-8a773a514f9f.png?resizew=167)
![](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/707a18a1cb508d28a73f95d41d1a89ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5621c78ba894e47b6161e27a664093a0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/8/3801d1a4-c7a6-4c1b-aceb-8a773a514f9f.png?resizew=167)
A.点E到![]() ![]() |
B.点F的轨迹是一个圆 |
C.![]() ![]() |
D.直线![]() ![]() ![]() |
您最近一年使用:0次
3 . 如图,四边形
为矩形,
≌
,且二面角
为直二面角.
平面
;
(2)设
是
的中点,
,二面角
的平面角的大小为
,当
时,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb49df05f2e31d005735c3f14a21d30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f253eece04f2d23e3fdc338f694ffd5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8dc6db50a9709c3f4d84eee7bdf1250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2082c80ef7a33d9d397afccddeeca9e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89c9c2c831a0552a7c934365bc49ad3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6570aee18d73762e18716bb9dd33109b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefd06c239145a2b6ae87a955aa51414.png)
您最近一年使用:0次
2024-02-01更新
|
1012次组卷
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3卷引用:重庆市缙云教育联盟2024届高三下学期第二次诊断性检测数学试题
名校
4 . 如图,在三棱锥
中,侧面
底面
,
,
是边长为2的正三角形,
,
分别是
的中点,记平面
与平面
的交线为
.
平面
;
(2)设点
在直线
上,直线
与平面
所成的角为
,异面直线
与
所成的角为
,求当
为何值时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.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/4fbfcae2cecc98e2d6c16dde6d3ec1c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829a1a887ceba13dd8551b1e3604bf6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9df740160690029ac1e730c85f20347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4820decdfaf6808eda1b625cc8aa0110.png)
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2024-06-10更新
|
563次组卷
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8卷引用:重庆市第八中学2022届高三下学期调研检测(七)数学试题
重庆市第八中学2022届高三下学期调研检测(七)数学试题湖南师范大学附属中学2022届高三下学期月考(七)数学试题山西大学附属中学校2023届高三下学期3月模块诊断数学试题云南省红河州建水实验中学2022-2023学年高一下学期4月考试数学试题(已下线)专题03 空间向量求角度与距离10种题型归类-【巅峰课堂】2023-2024学年高二数学上学期期中期末复习讲练测(人教A版2019选择性必修第一册)湖北省宜荆荆2024届高三下学期五月高考适应性考试数学试题 江苏省南通一中2023-2024学年高二年级数学下学期第二次月考(含答案)(已下线)立体几何与空间向量-综合测试卷B卷
名校
5 . 已知正方体
的棱长为
是侧面
内任一点,则下列结论中正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/f95dbd67-9ea1-4200-a8ce-acf21c784d5d.png?resizew=148)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f31a9a7ed32e6b4d3410ae2a4620466a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/f95dbd67-9ea1-4200-a8ce-acf21c784d5d.png?resizew=148)
A.若![]() ![]() ![]() |
B.若![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
名校
解题方法
6 . 如图甲,在矩形
中,
为线段
的中点,
沿直线
折起,使得
点为
的中点,连接
,如图乙.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/17/40d753e3-9722-418e-a8dc-8e099a6e081d.png?resizew=332)
(1)求证:
;
(2)线段
上是否存在一点
,使得平面
与平面
所成角的余弦值为
?若不存在,说明理由;若存在,求出
的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/438f5e0b08422b2f93d122341b3d7672.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d81d73077d45142f21ca67f80633f7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35cb5a59879bfa249b9896d3458d43b5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/17/40d753e3-9722-418e-a8dc-8e099a6e081d.png?resizew=332)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2f4946f86dce1600096f79d7716ea03.png)
(2)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/977a483bd52c08968f4097d10609be20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a261474cc7607d31a6324cb4df9c8896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826c728050e3378921442ace20269ef6.png)
您最近一年使用:0次
名校
解题方法
7 . 如图,已知矩形
中,
,
.点
为线段
上一动点(不与点
重合),将
沿
向上翻折到
,连接
,
.设
,二面角
的大小为
,则下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f656e1d1f68954e5f06de8958f6a9310.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/729684f958ad60b8e905fe1e1da53c03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce57e4e1dcd593712430c53e93de0372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6405e9a84b771505dfeaf4d7129d0fc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae1bdd731e2b62f6438e171301a00bcb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/28/319c8be2-8ee6-4cc1-b71e-4b3ac4daecf8.png?resizew=165)
A.若![]() ![]() ![]() |
B.若![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.点![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
2023-11-27更新
|
425次组卷
|
3卷引用:重庆市西南大学附属中学校2023-2024学年高三上学期期中考试数学试题
重庆市西南大学附属中学校2023-2024学年高三上学期期中考试数学试题重庆市第八中学校2023-2024学年度高二上学期检测六数学试题(已下线)第三章 折叠、旋转与展开 专题一 平面图形的翻折、旋转 微点8 平面图形的翻折、旋转综合训练
名校
8 . 如图,
是半球
的直径,
是底面半圆弧
上的两个三等分点,
是半球面上一点,且
.
(1)证明:
平面
:
(2)若点
在底面圆内的射影恰在
上,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c6eff038537d5fdae6e9741e2bd9dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36fa06464d2e58b414c503be9bcc711e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/23/1f60f440-52e0-4583-9354-fe09c0390742.png?resizew=181)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45fbffb9e2c7fa7c5006cde8da0cabe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c745df4f226027778d5fe45b6501b822.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e9f7d1272b7344346b58b660aa260a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
您最近一年使用:0次
2023-11-22更新
|
2611次组卷
|
9卷引用:重庆市缙云教育联盟2024届高三下学期2月月度质量检测数学试题
重庆市缙云教育联盟2024届高三下学期2月月度质量检测数学试题江苏省淮安、南通部分学校2023-2024学年高三上学期11月期中监测数学试题江苏省启东市2023-2024学年高三上学期期中质量监测数学试卷(已下线)模块六 全真模拟篇 拔高2 期末终极研习室(2023-2024学年第一学期)高三(已下线)第六套 九省联考全真模拟山东省菏泽市2024届高三上学期期末考试数学试题(B)(已下线)模块六 立体几何(测试)江苏省南通市海门中学2023-2024学年高二下学期3月阶段练习数学试卷江苏省南通市海安高级中学2023-2024学年高二下学期阶段检测(一)数学试题
名校
9 . 如图,在四棱台
中,底面
是正方形,
,
,
,
.
(1)求证:直线
平面
;
(2)求二面角
的余弦值.
![](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/d4c98d0a336e7b78a3164df8231ab050.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e90b10ae50e3cf8663038cdeb697168c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2a61472439de1ba85cfe33840b775f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/295aced98768ce261e00fe6660a427a2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/1/03e3086b-211f-478a-ae50-c6221513297d.png?resizew=169)
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee2b198824daf85c88054bda90664231.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce12587a7129e4a6ba2837214c6c4cdf.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0830c440cb5f1b816d17dcdebdba71a3.png)
您最近一年使用:0次
2023-10-12更新
|
770次组卷
|
3卷引用:重庆市渝北中学校2024届高三上学期12月月考数学试题
名校
10 . 在棱长为
的正方体
中,已知
为
的中点,点
为底面
上的动点,若
,则点
的轨迹长度为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](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/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b8a2de1d86ce80be87e8d10d1c90da8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-09-08更新
|
499次组卷
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3卷引用:重庆市永川萱花中学校2023-2024学年高三上学期期中考试数学试题
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