名校
解题方法
1 . 如图,四面体
中,
,
,
,E为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/a3e792b4-4cee-4a38-b232-ca71ce9ee967.png?resizew=169)
(1)证明:
⊥平面
;
(2)设
,
,
,点F在
上,若
与平面
所成角的正弦值为
,求点F到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89a6e9864194f5b8d6e0dc534376aef5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0383f8245ace6d1abbaada18d52c8c3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/a3e792b4-4cee-4a38-b232-ca71ce9ee967.png?resizew=169)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5322a78b02c2bc387ea7dce3e9461974.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041b85054f9442650fa5cf2e7dd1ef4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3ad39474bacab0f0ca9417460943b95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74fe624c03051fc4a81383888de774bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d78fc7fcb2762de28dcef8aa3aa0e49.png)
您最近一年使用:0次
名校
解题方法
2 . 如图,在正方体
中,棱长为2,M、N分别为
、AC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/b56008ba-9c08-4d69-b4f2-a76a19df14d6.png?resizew=145)
(1)证明:
平面
;
(2)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/b56008ba-9c08-4d69-b4f2-a76a19df14d6.png?resizew=145)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7592c4f01c8e06c7ee90df5b9413a9f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb04914c4e8fb3483da44c67fe1809f.png)
您最近一年使用:0次
3 . 如图,在四棱锥
中,
平面
,
为
的中点,
为
的中点,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/16/5139995d-07a7-49c5-b57d-657035ebbaa1.png?resizew=149)
(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/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c83f8945042b9c8fb2fbdac9308d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/defa5b53043ae802bb1af7d14374406d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9060f03b9ee41d70d135b1e1a8902ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829018a6ca0aff95d89e3f7cd943274e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46ff87836403b4cf4f728d5ac4d2c87a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/16/5139995d-07a7-49c5-b57d-657035ebbaa1.png?resizew=149)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d32e76582bf550593fdef53e081225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef796b46e68fe77b117ff0483d2370c.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef796b46e68fe77b117ff0483d2370c.png)
您最近一年使用:0次
名校
4 . 如图,在正方体
中,棱长为
分别是
的中点.
(1)证明:
.
(2)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/dd21f1df5df752343fd02502854eacb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd94e1bd480758d8ef0cd553e0361e62.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/12/a0debf21-a1d8-41ce-8460-b6d8b1a285f2.png?resizew=167)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f838933ac032270e24d15265461a89bd.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dab8375daa062d56ac9dcd77eebcf9f4.png)
您最近一年使用:0次
2023-12-15更新
|
236次组卷
|
14卷引用:海南省海口市秀英区海南枫叶国际学校2023-2024学年高二上学期期中数学试题
海南省海口市秀英区海南枫叶国际学校2023-2024学年高二上学期期中数学试题陕西省部分学校2023-2024学年高二上学期10月联考数学试题山东省聊城第一中学2023-2024学年高二上学期10月月考数学试题山东省部分学校2023-2024学年高二上学期10月质量检测联合调考数学试题陕西省西安市灞桥区2023-2024学年高二上学期第一次联考数学试题吉林省部分名校2023-2024学年高二上学期10月联考数学试题山东省泰安市肥城市第一高级中学2023-2024学年高二上学期10月月考数学试题陕西省部分学校(西安市第八十六中学等)2023-2024学年高二上学期10月联考数学试题广东省深圳市翠园中学2023-2024学年高二上学期期中数学试题陕西省榆林市第十中学2023-2024学年高二上学期期中数学试题湖北省武汉市汉阳区武汉情智学校2023-2024学年高二上学期11月期中考试数学试题安徽省蚌埠市五河致远实验学校、固镇汉兴学校2023-2024学年高二上学期11月期中联考数学试题福建省南平市浦城第一中学2023-2024学年高二上学期期中数学试题吉林省普通高中友好学校联合体2023-2024学年高二上学期第三十七届基础年级期中联考数学试题
解题方法
5 . 已知椭圆
,一组平行直线的斜率是
.
(1)求这组直线何时与椭圆有两个公共点?
(2)当它们与椭圆有两个公共点时,证明这些直线被椭圆截得的线段的中点在同一条直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f64b7ab668d61bcb8ec6d195c672a81e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
(1)求这组直线何时与椭圆有两个公共点?
(2)当它们与椭圆有两个公共点时,证明这些直线被椭圆截得的线段的中点在同一条直线上.
您最近一年使用:0次
解题方法
6 . 如图,在棱长为1的正方体
中,
分别为
的中点,点
在
上,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/7/33a57982-8056-4cf0-b736-7397ee7177af.png?resizew=158)
(1)求证:
;
(2)求
与
所成角的余弦值.
![](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/89b866a756d422faec0f7eb229dfaabf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0635059fd390592d1851dfe56c72cd6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/7/33a57982-8056-4cf0-b736-7397ee7177af.png?resizew=158)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d435974639ea2850bb5c21efe64b123b.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fec5bd77cfc1313bc200480cc66c766.png)
您最近一年使用:0次
2023-12-15更新
|
248次组卷
|
2卷引用:海南省琼海市海桂中学2023-2024学年高二上学期期中考试数学试题(B卷)
名校
7 . 如图,在棱长为3的正方体
中,点E,F分别是棱BC,
的中点,若直线
与平面AEF交于点M,则线段
的长度为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5563473602e1b17d582a165b7b7b6b2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/15/69d038c4-b2c3-4f77-bb4c-ba6ab80312b7.png?resizew=166)
A.![]() | B.2 | C.![]() | D.3 |
您最近一年使用:0次
名校
8 . 如图,边长为4的正方形
是圆柱的轴截面,点P为圆弧
上一动点(点P与点A, D不重合)
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6f9353ca110c8b81561455b232dbc15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9dcc19ff9096c3df816247fb8a81026.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/c6561a6b-8e36-46e4-92ef-ec95f25c0d85.png?resizew=142)
A.存在![]() ![]() |
B.三棱锥![]() ![]() |
C.当![]() ![]() ![]() ![]() |
D.直线![]() ![]() ![]() |
您最近一年使用:0次
名校
解题方法
9 . 已知直线
与椭圆
交于
两点,若点
恰为弦
的中点,则椭圆
的焦距为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f85317ebf501da5c726d17c5db30a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c6778c1f36528c7f59f3857b5aa089e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/530e5817131adf2c05b99ff18eb9060f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-11-29更新
|
405次组卷
|
3卷引用:海南省文昌市文昌中学、华迈实验中学2023-2024学年高二上学期期中段考数学试题
解题方法
10 . 三棱台
中,若
面
,
,
,
,
,
分别是
的中点.
(1)求证:
平面
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f90e17995e2f71e297d94ae51c7e5b1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9260ee90b4107dcdc5b2b0937c40e8c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3676391efa2ac62958c633b7943e746.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/20ddad7a-9ed7-4235-94cd-0ae962869862.png?resizew=153)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef2e72bc4f73790da7c76e46767b4fd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f96c673a2381f118ea2d3efc0bca1f3.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a3f5c4436466bed86c25c5f26ccbeb.png)
您最近一年使用:0次