名校
1 . 如图,在三棱锥
中,
,O为AC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/25/36d8828b-c19f-4629-9473-77426f0eaa9e.png?resizew=156)
(1)证明:
⊥平面ABC;
(2)若点M在棱BC上,且二面角
为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e69acb641788897805a6f99236da48a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/25/36d8828b-c19f-4629-9473-77426f0eaa9e.png?resizew=156)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
(2)若点M在棱BC上,且二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2547225b7d1f17b04a2077258be59ee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03e85ab30d1a7b29a5511f963991affc.png)
您最近一年使用:0次
2023-04-23更新
|
2883次组卷
|
10卷引用:上海市复兴高级中学2023届高三适应性练习数学试题
上海市复兴高级中学2023届高三适应性练习数学试题浙江省杭州第九中学2021-2022学年高二上学期期末数学试题广东省中山市民众德恒学校2022-2023学年高二上学期第一次段考数学试题河北省石家庄市十八中2022-2023学年高二下学期开学考试数学试题贵州省贵阳市五校2023届高三联合考试(五)理科数学试题福建省2022-2023学年高二上学期11月期中数学试题(已下线)数学(新高考Ⅰ卷)(已下线)数学(上海卷)(已下线)河北省石家庄市2023届高三质量检测(一)数学试题变式题17-22福建省永安市第九中学2023-2024学年高二上学期期中考试数学试题
解题方法
2 . 已知四棱锥
的底面
为正方形,且
平面
,
为
中点
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/7/8a51e8c0-34a6-4af4-9e41-5ba48f16a0ef.png?resizew=158)
(1)求证:面
面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
(2)求异面直线
与
所成角的大小
![](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/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b295c76f71f27716fd6ba9fabc453dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/7/8a51e8c0-34a6-4af4-9e41-5ba48f16a0ef.png?resizew=158)
(1)求证:面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
您最近一年使用:0次
2023-03-06更新
|
246次组卷
|
2卷引用:上海市虹口高级中学2023-2024学年高二上学期期末考试数学试题
名校
3 . 如图,在三棱柱
中,底面ABC是以AC为斜边的等腰直角三角形,侧面
为菱形,点
在底面上的投影为AC的中点D,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/20/453d1950-317a-4dd3-8175-4fde1a3d3ca0.png?resizew=183)
(1)若M、N分别为棱AB、
的中点,求证:
;
(2)求点C到侧面
的距离;
(3)在线段
上是否存在点E,使得直线DE与侧面
所成角的正弦值为
?若存在,请求出
的长;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/20/453d1950-317a-4dd3-8175-4fde1a3d3ca0.png?resizew=183)
(1)若M、N分别为棱AB、
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf4169667e0dd7c8b5824295177edb1b.png)
(2)求点C到侧面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
(3)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e27511b095e8e96719af8bc9a7412ac1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce1b066f8869d0ff4513f7a99745125.png)
您最近一年使用:0次
2023-01-15更新
|
1965次组卷
|
4卷引用:上海市华东师范大学第一附属中学2022-2023学年高二上学期期末数学试题
上海市华东师范大学第一附属中学2022-2023学年高二上学期期末数学试题(已下线)专题6 第3讲 立体几何中的向量方法(已下线)期末真题必刷基础60题(35个考点专练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(沪教版2020必修第三册)(已下线)第02讲:空间向量与立体几何交汇(必刷6大考题+7大题型)-2023-2024学年高二数学上学期《考点·题型·难点》期末高效复习(人教A版2019选择性必修第一册)
名校
解题方法
4 . 如图,在直三棱柱
中,
,点
、
分别为
、
的中点,
与底面
所成的角为arctan2.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/12/0c4d2d4e-c2ef-4882-b5b0-fa646c503dc3.png?resizew=155)
(1)求异面直线
与
所成角的大小(结果用反三角函数表示);
(2)求点
与平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a9ad711b25c36dae0c2a2cedff9954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/effe94e1c17a1af4575aa461275cdad6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42b618e1cd0f3a7c27816d86fbe3907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/12/0c4d2d4e-c2ef-4882-b5b0-fa646c503dc3.png?resizew=155)
(1)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/991a908f49f9deb228415dcb3d9248aa.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbc96c20ebba91031a1c54037fe651c.png)
您最近一年使用:0次
2022-11-06更新
|
265次组卷
|
10卷引用:上海市复兴高级中学2022届高三上学期10月月考数学试题
上海市复兴高级中学2022届高三上学期10月月考数学试题上海市浦东新区2021届高三三模数学试题上海市大同中学2021届高三三模数学试题上海市向明中学2022届高三上学期9月月考数学试题(已下线)考向23 点、直线、平面之间的位置关系-备战2022年高考数学一轮复习考点微专题(上海专用)上海市青浦高级中学2022届高三下学期4月线上质量检测数学试题沪教版(2020) 选修第一册 新课改一课一练 第4章 阶段复习2上海市青浦高级中学2022届高三4月质检数学试题(已下线)专题11空间向量与立体几何必考题型分类训练-2上海市南洋模范中学2022届高三上学期期中数学试题
名校
解题方法
5 . 如图1,在等腰直角三角形
中,
分别是
上的点,
为
的中点.将
沿
折起,得到如图2所示的四棱锥
,其中
.
![](https://img.xkw.com/dksih/QBM/2022/11/3/3101878167298048/3102546276319232/STEM/c06e270e3a814fb09ae101e1b01ac2a5.png?resizew=409)
(1)求证:
平面
;
(2)求二面角
的大小;(结果用反三角函数值表示)
(3)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3355a185c8777425df5d15a6276c1263.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5881068127a39caf319492b4177204f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e05431a2a292b824927c313916315670.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be7527d873655c33ebcd1f2b14a9315c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f75d881d8d0356e4c21c915423e6ddae.png)
![](https://img.xkw.com/dksih/QBM/2022/11/3/3101878167298048/3102546276319232/STEM/c06e270e3a814fb09ae101e1b01ac2a5.png?resizew=409)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d020a9a555c8992a24992d63a4981bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff0a49b9a3976893039103a7ba3727e1.png)
(3)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1530d93834fbafba5f7217778ea90442.png)
您最近一年使用:0次
名校
解题方法
6 . 已知正方体ABCD—
的棱长为4,M在棱
上,且
1,则直线BM与平面
所成角的正弦值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc689a0bf91e6384ca0bd3fb3fbfa0ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd26a89cc920539a40cee94d8529f0ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb04914c4e8fb3483da44c67fe1809f.png)
您最近一年使用:0次
2022-05-13更新
|
1582次组卷
|
6卷引用:上海市华东师范大学第一附属中学2022-2023学年高二上学期10月月考数学试题
上海市华东师范大学第一附属中学2022-2023学年高二上学期10月月考数学试题福建省漳州市2022届高三第三次质量检测数学试题江苏省南京师范大学附属中学2021-2022学年高二下学期期末模拟数学试题(已下线)专题09 空间向量与立体几何(已下线)第06讲 向量法求空间角(含探索性问题) (讲)-1(已下线)第三篇 努力 “争取”考点 专题6 空间角与距离【练】
名校
7 . 如图,已知菱形
中,
,直角梯形
中,
,
,
,
分别为
中点,平面
平面
.
![](https://img.xkw.com/dksih/QBM/2022/1/17/2896297974628352/2899174074638336/STEM/257929dcb40d4118a25ba7f82033be74.png?resizew=219)
(1)求证:
平面
;
(2)异面直线
与
所成角的大小;
(3)线段
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
的长;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b5d8835312ea8b07c0f6c7740fbef65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea04814d8e706040feac271b50b66c67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eed15d0ed75bf936f224f931da5d950.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac107155d65701fbbcd6b6740b510e46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04e650f493b12fda60ddb12fc32a3388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5e89423a12948f0fa4f9fe7adf956a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c674dc5024374f53920947c4cf4baf11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/2022/1/17/2896297974628352/2899174074638336/STEM/257929dcb40d4118a25ba7f82033be74.png?resizew=219)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeebdf3d00c146a1b4d220909d7573c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
(2)异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(3)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93f1918a4291dc32884eb3a9dbab1529.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
您最近一年使用:0次
名校
解题方法
8 . 如图,在圆柱
中,它的轴截面
是一个边长为2的正方形,点C为棱
的中点,点
为弧
的中点.
![](https://img.xkw.com/dksih/QBM/2021/11/21/2856261557362688/2857312744136704/STEM/71b1eea7-5160-4597-a5e5-52af8c104771.png?resizew=199)
(1)求异面直线OC与
所成角的大小;
(2)求直线
与圆柱
底面所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://img.xkw.com/dksih/QBM/2021/11/21/2856261557362688/2857312744136704/STEM/71b1eea7-5160-4597-a5e5-52af8c104771.png?resizew=199)
(1)求异面直线OC与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
您最近一年使用:0次
2021-11-23更新
|
268次组卷
|
2卷引用:上海市复兴高级中学2023届高三上学期开学考数学试题
名校
解题方法
9 . 如图,在正方体
中.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/12/575bc06b-e9a2-49ad-9740-9ed29408b544.png?resizew=159)
(1)求异面直线
和
所成角的大小;
(2)求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/12/575bc06b-e9a2-49ad-9740-9ed29408b544.png?resizew=159)
(1)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce93d167f4591e845358ee3190e1f7c.png)
您最近一年使用:0次
2021-11-14更新
|
543次组卷
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10卷引用:上海市鲁迅中学2022-2023学年高二上学期期中数学试题
上海市鲁迅中学2022-2023学年高二上学期期中数学试题上海交通大学附属中学2021-2022学年高二上学期期中数学试题上海市黄浦区大同中学2022届高三上学期12月月考数学试题上海市进才中学2022届高三下学期3月月考数学试题上海市大同中学2022-2023学年高二上学期期中数学试题(已下线)重难点01 空间角度和距离五种解题方法-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)(已下线)高二下期中真题精选(常考60题专练)-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)上海外国语大学附属浦东外国语学校2023-2024学年高二上学期期中考试数学试卷(已下线)期中真题必刷常考60题(22个考点专练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(沪教版2020必修第三册)(已下线)高二 期中模拟卷(原版卷)
10 . 已知如图①,在菱形ABCD中,
且
,
为AD的中点,将
沿BE折起使
,得到如图②所示的四棱锥
,在四棱锥
中,求解下列问题:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/37f4c6b5-72e1-46f0-b657-9b4bbebde8cc.png?resizew=366)
(1)求证:BC
平面ABE;
(2)若P为AC的中点,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cdf6426f0eaa95c31648895d35fe165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a88c44f558705de3bcefcfc0ece96b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5164a3cc47e266446d49127e2ef10c37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5164a3cc47e266446d49127e2ef10c37.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/37f4c6b5-72e1-46f0-b657-9b4bbebde8cc.png?resizew=366)
(1)求证:BC
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
(2)若P为AC的中点,求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/053af8641980763a7f0e77beefe0712d.png)
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2卷引用:上海市虹口区2020-2021学年高二下学期期末数学试题