名校
1 . 如图1,在平行四边形
中,
=60°,
,
,
,
分别为
,
的中点,现把平行四边形
沿
折起如图2所示,连接
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/3/b8e39710-99eb-4ef5-abe1-9a672673aa4c.png?resizew=396)
(1)求证:
;
(2)若
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883732ae71bfed76e07732ec709f4653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b5d693c4f0c4d0e6c0c810e7d464b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883732ae71bfed76e07732ec709f4653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa6cb992b6faad4744f85d73a3b76dd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a56f2e56229a722d1f40d74d3967a3d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/3/b8e39710-99eb-4ef5-abe1-9a672673aa4c.png?resizew=396)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82c2b3adb41e8965f553da2e5086a751.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a677b42f8b427b21924a559b90141d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c44507c93f6180afd1697d2fa5a5c741.png)
您最近一年使用:0次
2021-06-15更新
|
1645次组卷
|
12卷引用:广东省广州市广州大学附属中学2021-2022学年高二上学期第一次月考数学试题
广东省广州市广州大学附属中学2021-2022学年高二上学期第一次月考数学试题广东省真光中学2021-2022学年高二上学期10月月考数学试题2016届福建福州市高三上学期期末数学(理)试卷2017届河南南阳一中高三理上学期月考四数学试卷宁夏石嘴山市第三中学2017届高三下学期第三次模拟考试数学(理)试题河南省南阳市2018届高三期终质量评估数学(理)试题广西南宁二中2020届高三4月开学考试理数试题四川省成都市实验外国语学校2020届高三(高2017级)数学模拟(三)理试题(已下线)专题19 立体几何综合-2020年高考数学(理)母题题源解密(全国Ⅲ专版)湖北省武汉一中2021届高三下学期二模数学试题(已下线)2022年高考考前20天终极冲刺攻略(三)【理科数学】 (5月27日)2023版 北师大版(2019) 选修第一册 突围者 第三章 专项拓展训练3 用空间向量解决折叠问题
2 . 如图,在正三棱柱ABC-A1B1C1,底面△ABC的边长AB=1,侧棱长为
,P是A1B1的中点,E、F、G分别是AC,BC,PC的中点.
![](https://img.xkw.com/dksih/QBM/2019/1/13/2118008030846976/2118564053876736/STEM/221139ce-b766-47b9-b740-b0ee85414aef.png)
(1)求FG与BB1所成角的大小;
(2)求证:平面EFG∥平面ABB1A1.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca9c6fe12d3a9727e00ef87a630302ab.png)
![](https://img.xkw.com/dksih/QBM/2019/1/13/2118008030846976/2118564053876736/STEM/221139ce-b766-47b9-b740-b0ee85414aef.png)
(1)求FG与BB1所成角的大小;
(2)求证:平面EFG∥平面ABB1A1.
您最近一年使用:0次
2019-01-14更新
|
715次组卷
|
3卷引用:广东省东莞市嘉荣外国语学校2023-2024学年高二上学期期中数学试题
11-12高三上·广东佛山·阶段练习
解题方法
3 . 如图,在棱长为1的正方体
中,
为线段
上的点,且满足
.
(Ⅰ)当
时,求证:平面
平面
;
(Ⅱ)试证无论
为何值,三棱锥
的体积恒为定值;
(Ⅲ)求异面直线
与
所成的角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d5a7b6a93211567783abf11ee3012db.png)
(Ⅰ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500d68f2678989a5ce7431cfd51b019d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1f5e22b37cea8a05fa13f85414c7c52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ca5b5fd1031438de2d2dd59be8c348.png)
(Ⅱ)试证无论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbf24f4e2a22bf61c8e14bdaf57b7b77.png)
(Ⅲ)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c407eeb34204a1df967b8fbe481cb04d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd4c85bb98a2a0afddd7ed92578ad2e.png)
![](https://img.xkw.com/dksih/QBM/2011/12/18/1570621624582144/1570621630103552/STEM/81711ac1-f1d4-4a98-b455-ad2492e47f04.png?resizew=182)
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