名校
1 . 如图,在四棱锥
中,平面
平面PAD,
,
,正三角形PAD的边长为2.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/24/63ef7254-7a9c-450d-afe9-8204271e4a1c.png?resizew=162)
(1)求证:
平面PAD;
(2)若
,
,求平面PAD与平面PBC所成的锐二面角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/413c799e8fb983e6274ec4be9ff6c431.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/24/63ef7254-7a9c-450d-afe9-8204271e4a1c.png?resizew=162)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833cfda415649b832cc136caed392753.png)
您最近一年使用:0次
名校
2 . 如图,在三棱柱
中,侧面
为正方形,
;设M是
的中点,满足
,N是BC的中点,P是线段
上的一点.
(1)证明:
平面
;
(2)若
,
,求直线
与平面PMN所成角的大小.
![](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/a566b100fb2ebe3d208f9b6527934218.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2027fa3dfcde1373ca0222e1358e0c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/12/e6f1d103-14a1-4a6c-8261-f1a5cc952c65.png?resizew=182)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0edb1508fc95765f3bb316bcb5252d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/105347676853328617bf64545d8546cb.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d768ffd5bf75080e8ff5ce6b472c0cc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4f68b8069f0df9e3dbe15c3d7cf5052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
您最近一年使用:0次
2023-12-12更新
|
361次组卷
|
2卷引用:上海市虹口区2024届高三上学期期终学生学习能力诊断测试数学试题
3 . 如图,三棱锥
中,
,
,
,E为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/27/73000cff-6b06-4c1f-9297-0cc7d5fdc277.png?resizew=186)
(1)证明:
;
(2)点F满足
,求平面
和平面
所成的锐二面角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d3d6fb3406ff7fabf9c3b5c7541c67d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff9c7cbcc38b28d45c8539710e5b260a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d495d6bb2cf4e141d2055a9f7072018.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/27/73000cff-6b06-4c1f-9297-0cc7d5fdc277.png?resizew=186)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0de882caea347e2bd6fcd426caa13b8.png)
(2)点F满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028a14cd09c33f7e6d9fdc184b5fe64b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ddc76d96d6951ebfef3fe63892a1114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/437bc0b5b7815c77b4956f194fc6ef52.png)
您最近一年使用:0次
解题方法
4 . 如图所示,在正方体
中,E为线段
上的动点,则下列直线中与直线CE夹角为定值的直线为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/27/e9624614-ef43-4edd-8de1-fd9afb2ff006.png?resizew=167)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/27/e9624614-ef43-4edd-8de1-fd9afb2ff006.png?resizew=167)
A.直线![]() | B.直线![]() |
C.直线![]() | D.直线![]() |
您最近一年使用:0次
5 . 如图,已知正方形ABCD和矩形ACEF所在的平面互相垂直,
,
,M是线段EF的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/3/3958a892-d10d-47f4-a666-da956c78f6c0.png?resizew=177)
(1)求证:
;
(2)求证:
平面BDE;
(3)求二面角
的大小.(用反三角表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0cee0f36dc452e58086832c0152b641.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/3/3958a892-d10d-47f4-a666-da956c78f6c0.png?resizew=177)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e46ba5224d2f60ef6938717a4c48ccd.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f33fa5152ba27f7b8a28890cefca219.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4019805fed3b6cca619f4035e7618cd0.png)
您最近一年使用:0次
解题方法
6 . 已知正方体
中,棱长为1,求
(1)异面直线AB与
所成角;
(2)直线
与平面ABCD所成角;(用反三角表示)
(3)矩形
绕直线
旋转一周所得几何体的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/3/3323cd1b-c1c4-4c91-ac89-5f031601c040.png?resizew=168)
(1)异面直线AB与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e539f26ed5e0b20ff7220559324869a4.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
(3)矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
您最近一年使用:0次
名校
7 . 如图,设
是底面为矩形的四棱锥,
平面
.
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/2/90640926-e2b5-46e7-9917-9e17876e68f5.png?resizew=164)
(1)若
,求四棱锥
的体积;
(2)若直线
与平面
所成的角的大小为
,求直线
与平面
所成的角的大小.
![](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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f83a04565a8ebaa111894b724b0ba266.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/2/90640926-e2b5-46e7-9917-9e17876e68f5.png?resizew=164)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4125524caac016727c80d2722c5ba3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b675e591d474c5a777a728b4df96b603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
名校
解题方法
8 . 如图,在三棱柱
中,底面
是以
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
的中点
,且
.
(1)求证:
;
(2)求点
到侧面
的距离;
(3)在线段
上是否存在点
,使得直线
与侧面
所成角的余弦值为
?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/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/19/72c4c98d-ee41-4e09-9044-82670098fcd2.png?resizew=179)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a382ccd078374f1efebb26a43599e596.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.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
2023-10-18更新
|
949次组卷
|
9卷引用:上海市虹口区2023届高考一模数学试题
上海市虹口区2023届高考一模数学试题(已下线)专题08 立体几何解答题常考全归类(精讲精练)-1天津市梧桐中学2022-2023学年高三上学期期末数学试题(已下线)专题8-2 立体几何中的角和距离问题(含探索性问题)-3(已下线)6.3.4空间距离的计算(3)上海市行知中学2023-2024学年高二上学期10月月考数学试题(已下线)湖南省长沙市长郡中学2024届高三上学期月考(二)数学试题变式题19-22(已下线)考点13 立体几何中的探究问题 2024届高考数学考点总动员【练】(已下线)专题06 用空间向量研究距离、夹角问题10种常见考法归类 - 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教A版2019选择性必修第一册)
名校
解题方法
9 . 已知
、
分别是正方体
的棱
、
的中点,求:
(1)
与
所成角的大小;
(2)二面角
的大小;
(3)点
在棱
上,若
与平面
所成角的正弦值为
,请判断点
的位置,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/26/272cab81-ee03-427b-8075-168f579977ce.png?resizew=142)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8eb4a9f462ca0c1d49c3fe91e720d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
(2)二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1d945b178e6db6fa78e3fe5610b2d39.png)
(3)点
![](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/9399c9a2a31b0e3165aea2d6ccc4f7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9961e091f180e964a962adf6916f33c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffb71379c2a28a42f454ec4f3cf01a67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
2023-06-20更新
|
646次组卷
|
6卷引用:上海市复兴高级中学2023-2024学年高二上学期期中数学试题
上海市复兴高级中学2023-2024学年高二上学期期中数学试题上海市宝山区2022-2023学年高二下学期期末数学试题(已下线)第11讲 用空间向量研究距离、夹角问题11种常见考法归类-【暑假自学课】2023年新高二数学暑假精品课(人教A版2019选择性必修第一册)(已下线)专题1.6 空间角的向量求法大题专项训练(30道)-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第一册)上海大学附属中学2023-2024学年高二上学期9月月考数学试题上海市宝山区上海师大附属宝山罗店中学2023-2024学年高二下学期第一次诊断性测试(3月)数学试卷
名校
解题方法
10 . 已知
和
所在的平面互相垂直,
,
,
,
,
是线段
的中点,
.
(1)求证:
;
(2)设
,在线段
上是否存在点
(异于点
),使得二面角
的大小为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ae752bc1732e638f35cc08e347a5b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a7b5adfcac0f46a4cd19da4ebb4a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fffa3d9c32da53b0ea0c338012ea20c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d783fe7f3ce673d5d21281174e7a7968.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4151e948feebdf7b91fbe739feafa9bc.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30b0393ce62b24aa5f9b740d4cc6743b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4b820c84570da9c38d0a81c22788b76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
您最近一年使用:0次
2023-05-31更新
|
611次组卷
|
3卷引用:上海市虹口高级中学2023-2024学年高二上学期期中数学试题