1 . 已知等边
的边长为2,将其绕着
边旋转角度
,使点
旋转到
位置.记四面体
的内切球半径和外接球半径依次为
,当四面体
的表面积最大时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc414210eac238504494ce83becf6a8c.png)
__________ ;![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2187de07874b5370c4489cb4a2dff0b1.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0991d38c6edebb9740ab1061437c720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dce64d610e7f309e414d9abe7ff2e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0991d38c6edebb9740ab1061437c720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc414210eac238504494ce83becf6a8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2187de07874b5370c4489cb4a2dff0b1.png)
您最近一年使用:0次
2023-07-25更新
|
668次组卷
|
4卷引用:云南省保山市部分校2022-2023学年高二下学期期末模拟测试数学试题
云南省保山市部分校2022-2023学年高二下学期期末模拟测试数学试题广东五校2022-2023学年高二下学期期末联考数学试题(已下线)第11章 简单几何体(压轴必刷30题专项训练)-【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)第三章 折叠、旋转与展开 专题一 平面图形的翻折、旋转 微点3 翻折、旋转中的基本问题(三)
2 . 已知边长为2的菱形
中,
,将
沿
翻折,连接
,
,设点
为
的中点,点
在平面
上的投影为
,二面角
的大小为
.下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a466276f3b4a9a59addcaa6f68b6a850.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ac5396c5ea442e0364b50c1db3d2da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b977da2be0fc44742bd313eea1c30997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f0ac3005d5ecd6d4cea0ce99a47ef3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
A.在翻折过程中,点![]() ![]() |
B.在翻折过程中,直线![]() ![]() |
C.在翻折过程中,三棱锥![]() ![]() |
D.在翻折过程中,三棱锥![]() ![]() |
您最近一年使用:0次
3 . 已知正三棱锥
,顶点为
,底面是三角形
.
,且两两成角为
,设质点W自
出发依次沿着三个侧面移动环绕一周直至回到出发点
,求质点移动路程的最小值;
(2)若该三棱锥的所有棱长均为
,试求以
为顶点,以三角形
内切圆为底面的圆锥的体积;
(3)若该锥体的体积为定值
,求这三棱锥侧面与底面所成的角
,使该三棱锥的表面积
最小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7795e323d0890e17ca4101c196b9b053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若该三棱锥的所有棱长均为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(3)若该锥体的体积为定值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
您最近一年使用:0次
2021-11-19更新
|
1730次组卷
|
3卷引用:上海市徐汇中学2021-2022学年高二上学期期中数学试题
上海市徐汇中学2021-2022学年高二上学期期中数学试题上海海事大学附属北蔡高级中学2022-2023学年高二上学期12月月考数学试题(已下线)第11章 简单几何体(单元重点综合测试)-2023-2024学年高二数学单元速记·巧练(沪教版2020必修第三册)
20-21高二上·江西南昌·阶段练习
4 . 如图所示,在正方体
中,点G在棱
上,且
,点
、
、
分别是棱
、AB、BC的中点,P为线段
上一点,
.
![](https://img.xkw.com/dksih/QBM/2020/11/1/2583456102907904/2583535576391680/STEM/82bcf07b840242dc9c2d9a0ad9f2e648.png?resizew=185)
(Ⅰ)若平面
交平面
于直线
,求证:
;
(Ⅱ)若直线
平面
.
(ⅰ)求三棱锥
的表面积;
(ⅱ)设平面
与棱
交于点Q,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fbafedc202bd0d86c4dfdece9f8f4fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f01d1dd10776b00e9df008f03f2608c.png)
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cdc08e1c4a04a18d5ecea03393e36d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://img.xkw.com/dksih/QBM/2020/11/1/2583456102907904/2583535576391680/STEM/82bcf07b840242dc9c2d9a0ad9f2e648.png?resizew=185)
(Ⅰ)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7a447dc58e10adb7c8014071651e7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b54387f870ae37f7951b253665d64f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22ba669c69462fbbff2ef12ea9015fc8.png)
(Ⅱ)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/565133e91e3ace2b2187cfc6f1db5be6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7a447dc58e10adb7c8014071651e7c9.png)
(ⅰ)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b03980f99fa0f339388e564466e8b94.png)
(ⅱ)设平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbf62b9fe96ad0b0f58c8b3ba3075ab5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a4a7ba7546acc68f9cff46f1c53557f.png)
您最近一年使用:0次
名校
5 . 已知单位向量
两两的夹角均为
(
,且
),若空间向量
满足
,
,则有序实数组
称为向量
在“仿射”坐标系
(O为坐标原点)下的“仿射”坐标,记作
,有下列命题:
①已知
,
,则
;
②已知
,
,其中
,则当且仅当
时,向量
的夹角取得最小值;
③已知
,
,则
;
④已知
,
,
,则三棱锥
的表面积
.
其中真命题为________ (写出所有真命题的序号).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ddad20bb28660b1469acdb5440fa072.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dcadd1781ee9177e9bc76ce48afdd0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50774cbd8f44e5cff06dc7ecaa6bf94e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ad2e0f39e291976fcffd82bd5182c13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83fe554772fa28cae4c9233bde930b2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4949663ae37a5fa4417edacedd316762.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d685c54089867c395a4c49ba01b1237.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ad2e0f39e291976fcffd82bd5182c13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5e336d6ca2cae3d6e6c3810d7e521a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a712734f9668a5ad80a0c488cd2147e.png)
①已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c8a9bee1b188009aa812754ee06506b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d5852b277cf9c452ca1bea838b30290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d25325b09595d8e6ebe66e5140323ef8.png)
②已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/268dc3e270189059630d16e1b4ec4bf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f158d248d90b3be8a60abfa97f72c73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f57f35fbbb5d288691dda630a44961.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b9d5aaaceaa3ac514d17fcfefbf9b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/019c62d43430ababccb0fe08a55c6ec0.png)
③已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73371f19cb48256d4dcbbab055c2993f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e730da293b8ca1e22bf38e6846dc3ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ed5928e612316d6203f2e39e15d37b7.png)
④已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88d7d036775ba1a4fa27b15cba598f4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31b84c4fb07ceba134f667619a492bcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c6cee41ea9f8642ea78f6f6da7b8827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4278c0911e7df78965e78cff69cac5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d97de2e90bb2bccefe5039c193429cfc.png)
其中真命题为
您最近一年使用:0次
2019-08-17更新
|
2099次组卷
|
10卷引用:2015届福建省泉州一中高三下学期最后一次模拟理科数学试卷
2015届福建省泉州一中高三下学期最后一次模拟理科数学试卷2015-2016学年江西吉安一中高二上第一次段考理科数学卷【全国市级联考】四川省南充市2018届高三第三次联合诊断考试数学理科试题智能测评与辅导[理]-空间向量与立体几何2020届浙江省杭州市高三下学期4月统测模拟数学试题(已下线)专题06 空间向量与立体几何(难点)-2020-2021学年高二数学下学期期末专项复习(北师大版2019选择性必修第一册、第二册)江西省泰和中学2021-2022学年高二上学期第一次段考数学(理)试题沪教版(2020) 选修第一册 精准辅导 第3章 3.3 空间向量的坐标表示福建省福清西山学校2023-2024学年高二上学期9月月考数学试题(已下线)第3章 空间向量及其应用 单元综合检测(难点)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)