1 . 已知平面四边形
中,
,现将
沿
折成一个四面体,则当四面体的外接球表面积最小时,异面直线
与
所成角的余弦值是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b08f0afde7f0a296215845f36d6279b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
您最近一年使用:0次
名校
解题方法
2 . 直三棱柱
中,
分别为
,
的中点,点
是棱
上一动点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dfbab1e71852936206dfb76c891cb5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fe06eea0107d3d2991dc2fa02fc93b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
A.对于棱![]() ![]() ![]() |
B.棱![]() ![]() ![]() ![]() |
C.对于棱![]() ![]() ![]() ![]() ![]() |
D.棱![]() ![]() ![]() |
您最近一年使用:0次
2022-06-26更新
|
842次组卷
|
2卷引用:浙江省湖州市2021-2022学年高二下学期期末数学试题
名校
解题方法
3 . 如图,三棱柱
中,点
在平面
内的射影
在线段
上,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/28/23922da5-ee67-40b1-9d02-4dcaca87f354.png?resizew=257)
(1)证明:
;
(2)设直线
与平面
所成角为
,求二面角
的平面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ea07c1e3aea17f104399edabbab9861.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/28/23922da5-ee67-40b1-9d02-4dcaca87f354.png?resizew=257)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1515a445310d259a080d02e16c2e58e.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9c6ee40dff32baf8ffbf3cd4562c25a.png)
您最近一年使用:0次
2022-06-26更新
|
1353次组卷
|
3卷引用:浙江省湖州市2021-2022学年高二下学期期末数学试题
解题方法
4 . 棱长均为1的正三棱锥
中,
分别是棱
的中点,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a94d59dee2d5a8f0425b64b2083825.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a5f302c1c2f7e1b46cad05594ed672e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/484daa6752e055f12208bf70ce99571f.png)
A.![]() | B.平面![]() ![]() |
C.![]() | D.异面直线![]() ![]() ![]() |
您最近一年使用:0次
解题方法
5 . 正方体
中,下列判断错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
解题方法
6 . 长方体的一条体对角线与它一个顶点处的三个面所成的角分别为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61ba63ad02b1d5af2982fac3d91eb15c.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
7 . 如图,已知四棱锥
,底面
是矩形,
,点
是棱
上一劫点(不含端点).
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/7e95b680-cf15-4030-9d28-ee8c81b15ef2.png?resizew=222)
(1)求证:平面
平面
;
(2)当
且
时,若直线
与平面
所成的线面角
,求点
的运动轨迹的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebfcf34539673d516eb9b259951a81ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c047e537a6a747e508a6f2db2c58feb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a392d05d3cfcbb438569b1ea9980dc2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/7e95b680-cf15-4030-9d28-ee8c81b15ef2.png?resizew=222)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d28c625d7ac6878957facc8274d459c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49cfd630472bc73bd8c2209376dbe9d1.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ea14cf7efd7abd3f362281bae728b1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f072a9f8e8910d40065bde5d97938ea4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a392d05d3cfcbb438569b1ea9980dc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b3d44450540d2a9ecc93baefd1ba530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
您最近一年使用:0次
2022-06-26更新
|
1022次组卷
|
5卷引用:浙江省湖州市2021-2022学年高一下学期期末数学试题
浙江省湖州市2021-2022学年高一下学期期末数学试题江西省新余市第一中学2022-2023学年高二(零班)上学期开学考试数学试题江西省新余市第一中学2022-2023学年高二上学期开学考试数学试题浙江省温州第二高级中学2022-2023学年高二上学期10月学科素养测试数学试题(已下线)第三章 空间轨迹问题 专题五 微点2 翻折、旋转问题中的轨迹问题综合训练【培优版】
名校
解题方法
8 . 如图,在四棱锥
中,
平面
,
是等边三角形.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/426a2094-da06-4c04-9b1f-67fbca8c931e.png?resizew=188)
(1)证明:平面
平面
.
(2)求二面角
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/3e3027e0773dca6c712587bc7dbc8105.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/426a2094-da06-4c04-9b1f-67fbca8c931e.png?resizew=188)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1069d514c3c32aeabd274475ee209ed6.png)
您最近一年使用:0次
2022-01-24更新
|
2240次组卷
|
14卷引用:浙江省湖州市2022-2023学年高三上学期期末数学试题
浙江省湖州市2022-2023学年高三上学期期末数学试题浙江省湖州市安吉高级中学2022-2023学年高三上学期期末数学试题广东省湛江市2021-2022学年高二上学期期末数学试题山东省部分学校联考(烟台市第二中学等校)2021-2022学年高三上学期阶段质量检测数学试题陕西省安康市2021-2022学年高二上学期期末理科数学试题云南省楚雄州2022届高三上学期期末教育学业质量监测数学(理)试题(已下线)高二上学期期末【常考60题考点专练】(选修一+选修二)-2022-2023学年高二数学考试满分全攻略(人教A版2019选修第一册)云南省楚雄彝族自治州牟定县第一高级中学2022届高三上学期期末数学(理)试题福建省莆田市2022届高三第一次教学质量检测数学试题(已下线)三轮冲刺卷02-【赢在高考·黄金20卷】备战2022年高考数学模拟卷(新高考专用)(已下线)上海市华东师范大学第二附属中学2022-2023学年高二下学期5月月考数学试题云南省昆明市行知中学2022-2023学年高二上学期2月月考数学试题河南省郑州市宇华实验学校2024届高三上学期第一次模拟数学试题(已下线)专题04 立体几何
9 . 如图,四边形
为梯形,
,
,
,
,
,点
在
上,且
.现沿
将
折起至
的位置,使
.
![](https://img.xkw.com/dksih/QBM/2022/4/15/2958751621644288/2962082452348928/STEM/4d626cfe-ca26-4782-8af8-27c64e3dbbba.png?resizew=343)
(1)求证:
平面
;
(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/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/953f11eb95bfc036d85b472f81c6fb4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eca7e1a727ba332984ad857b3d25344d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80b6d3947d1ac5a2942ae58183acedf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7f9fba8a4098c1a0515286eb8d616dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e340674361f3742dd118ccc82d23c741.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16dbbc3b3b87c64f4570b068749228b1.png)
![](https://img.xkw.com/dksih/QBM/2022/4/15/2958751621644288/2962082452348928/STEM/4d626cfe-ca26-4782-8af8-27c64e3dbbba.png?resizew=343)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/604a7e1e37d514c1dd84b07d85e7cbe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0760712e3e2ea02b755b751e760d0c55.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/642401af2d7fc2de640ff7f6a8715950.png)
您最近一年使用:0次
2022-04-20更新
|
537次组卷
|
4卷引用:浙江省湖州市2020-2021学年高二上学期期末数学试题
10 . 如图,在四棱锥
中,底面
为矩形.
平面
,
,当
分别为
的中点.
![](https://img.xkw.com/dksih/QBM/2022/1/5/2887935234629632/2892801177100288/STEM/72b38fa1-d619-4006-bebb-a4c3d85e8d34.png?resizew=219)
(1)求证:
平面
;
(2)若
且
,平面
与平面
所成锐二面角的余弦值为
,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f95475bfc06e884754eb4a455c3f434e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a109c829d652632a88ade6924fcda206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf9b288c48c73463a2f214f02b6952a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d79f6bec0d2dab9b9efedfe86d1159b1.png)
![](https://img.xkw.com/dksih/QBM/2022/1/5/2887935234629632/2892801177100288/STEM/72b38fa1-d619-4006-bebb-a4c3d85e8d34.png?resizew=219)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2b4e753ef119608188c46a50ec597e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fdb3db261e7b227c2d853499b27ddc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25ab5f5620270e7a9a4218d921325b5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64e76a4c1e5934f51cdca2ffbc8313f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
您最近一年使用:0次
2022-01-12更新
|
500次组卷
|
5卷引用:浙江省湖州市安吉县天略外国语学校2022届高三上学期期末模拟数学试题
浙江省湖州市安吉县天略外国语学校2022届高三上学期期末模拟数学试题陕西省渭南市集才中学老城分校2021-2022学年高三上学期期末理科数学试题浙江省绍兴市诸暨海亮高级中学2021-2022学年高三上学期选考模拟最后一测数学试题浙江省绍兴市诸暨海亮高级中学2021-2022学年高三上学期1月测试数学试题(已下线)专题21 空间向量与立体几何解答题20题-备战2022年高考数学冲刺横向强化精练精讲(新高考专用)