名校
解题方法
1 . 如图所示,在棱长为2的正方体
中,
分别为线段
的中点.
与
所成的角;
(2)求三棱锥
的体积.
![](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/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1be192377dae2ccbf1e0348b5bdd8bd7.png)
您最近一年使用:0次
2023-01-03更新
|
353次组卷
|
7卷引用:上海市金山中学2018-2019学年高二下学期3月月考数学试题
名校
解题方法
2 . 如图,四边形
是正方形,
平面
,
,
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/a7ca64d7-6b34-4cb4-92e2-581ed54e1a82.png?resizew=169)
(1)求证:
;
(2)求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/a04f81be1cc59086cda63a2dc312c896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82465b63174087aeba7788ed984583d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07dd741bc3f02d8552afbcf63fba4fb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/a7ca64d7-6b34-4cb4-92e2-581ed54e1a82.png?resizew=169)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f392902d611863c6908a48e696e7bd8f.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/729a3ac9d8a312996c1aa9eb2e1959fa.png)
您最近一年使用:0次
2022-12-28更新
|
544次组卷
|
6卷引用:上海市曹杨第二中学2021届高三下学期3月月考数学试题
名校
解题方法
3 . 已知正方体
中,M,N分别为棱AB,
的中点,过
,M,N三点作该正方体的截面,若截面为一个多边形
,则
在顶点
处的内角的余弦值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/ffecf1fa-063b-4156-a9b0-67675f7715a7.png?resizew=150)
您最近一年使用:0次
2022-12-25更新
|
402次组卷
|
7卷引用:上海市南洋模范中学2022-2023学年高二上学期12月月考数学试题
上海市南洋模范中学2022-2023学年高二上学期12月月考数学试题(已下线)上海市高二上学期【第一次月考卷】(测试范围:第10章-第11章)-【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)河北省高碑店市崇德实验中学2022-2023学年高二上学期期末数学试题(已下线)6.3.3空间角的计算(3)(已下线)高二上期中真题精选(易错60题30个考点专练)【考题猜想】-2023-2024学年高二数学上学期期中考点大串讲(人教A版2019选择性必修第一册)(已下线)专题05用空间向量研究距离、夹角问题(2个知识点6种题型1个易错点1种高考考法)(3)(已下线)第二章 立体几何中的计算 专题四 空间几何体截面问题 微点5 空间几何体截面问题综合训练【培优版】
名校
4 .
为正方体,动点P在对角线
上,记
.
(1)求证:
;
(2)若异面直线AP与
所成角为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd445c6377d1ced1f8aa34f5c772b24b.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a0dba7306bdaf6e1011c146dea29172.png)
(2)若异面直线AP与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7dfd4c4648dc52d0952c20f3978fadd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
名校
5 . 如图,在四棱锥
中,已知
底面
,底面
是正方形,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/24/285f4179-33d6-4104-a2e5-1913d3ba5aa2.jpg?resizew=172)
(1)求证:直线
平面
;
(2)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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829f9180ddd9aa1a0ee0dc520f4e0b5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/24/285f4179-33d6-4104-a2e5-1913d3ba5aa2.jpg?resizew=172)
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
您最近一年使用:0次
2022-12-23更新
|
920次组卷
|
6卷引用:上海市宝山区上海师大附属罗店中学2023-2024学年高二上学期第二次诊断调研数学试题
名校
解题方法
6 . 如图,在四棱锥
中,底面
是菱形,
平面
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/dc98f5fc-f7f4-49c8-bef7-85f146b0dbd2.png?resizew=166)
(1)若
,求二面角
的大小;
(2)试求四棱锥
的体积V的取值范围.
![](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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/042d8524e9012bc8ade8c6a36c4cae24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01dcbd171693a47c5b932a5e84de10c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1ba63d0f1c98ac75fc39cca55c149c3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/dc98f5fc-f7f4-49c8-bef7-85f146b0dbd2.png?resizew=166)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70ad7d1e3fad77908415415d6b2a90f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a438393ddfc7da1804baf4932442bb35.png)
(2)试求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
您最近一年使用:0次
名校
解题方法
7 . 在正四面体
中,点E在棱AB上,满足
,点F为线段AC上的动点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a02c25b95e61557eec096de150ab873f.png)
A.存在某个位置,使得![]() |
B.存在某个位置,使得![]() |
C.存在某个位置,使得直线DE与平面DBF所成角的正弦值为![]() |
D.存在某个位置,使得平面DEF与平面DAC夹角的余弦值为![]() |
您最近一年使用:0次
2022-12-03更新
|
1312次组卷
|
4卷引用:上海市奉贤中学2023-2024学年高二上学期10月月考数学试题
上海市奉贤中学2023-2024学年高二上学期10月月考数学试题河南省许昌市禹州市高级中学2022-2023学年高二上学期12月期末数学试题湖北省武汉市部分重点中学2022-2023学年高二上学期期中联考数学试题(已下线)期中真题必刷压轴60题(18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(人教A版2019选择性必修第一册)
名校
解题方法
8 . 我国古代将四个面都是直角三角形的四面体称作鳖臑,如图,在鳖臑
中,
平面
,
是等腰直角三角形,且
,则异面直线
与
所成角的正切值为______ .(写出一个值即可,否则有两个答案)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6deecf9ccb7b7879455050633219e09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97dbde911bfb895b569ef5798280e44f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/d96b6d1f-5e41-4848-9da7-a3d7ace4ee4d.png?resizew=163)
您最近一年使用:0次
名校
9 . 如图,在直棱柱
中,
,
,D,E,F分别是
,
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/c5e4e7b8-5d4f-4fa3-8bf9-675045f1e0e6.png?resizew=165)
(1)求证:
;
(2)求
与平面DEF所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/002c709e9fee8d477bddfe595cc760f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8bd8c13192ca45c16dad5d59b547220.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/c5e4e7b8-5d4f-4fa3-8bf9-675045f1e0e6.png?resizew=165)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61fe81d0b136fc2acc97ab50ffbf6edf.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
您最近一年使用:0次
2022-11-25更新
|
551次组卷
|
3卷引用:上海市青浦高级中学2024届高三上学期10月质量检测数学试题
10 . 如图,平面
平面
,
,直线AM与直线PC所成的角为
,又
.
;
(2)求二面角
的大小;
(3)求多面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a68ab5e0937dcaf859ae5618b45b72a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/787ac5e13622afab5e9f8603afe42356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/436c114155b2c958b35ab9bf5920d618.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b7fc62b34350a8996c352f612329e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/901c9e0d6c246c195b65100f3f622899.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2e9ac46aabe38e5ea1a8cb0febc98af.png)
(3)求多面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4163c6228b9aa921450814bc6e47850d.png)
您最近一年使用:0次
2022-11-24更新
|
2048次组卷
|
3卷引用:上海市奉贤区致远高级中学2022-2023学年高二上学期12月月考数学试题