1 . 正四面体
的棱长为6,点
是该正四面体内切球球面上的动点,当
取得最小值时,
的面积为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/992907998c85cf872f6e66df0b0c1030.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
您最近一年使用:0次
解题方法
2 . 如图,四面体
中,
,
,
,
,
,
分别是
,
的中点,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/404728d0ea2699c71e674f30dd984abd.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/116aa36f6a9332fa772a35c6028f5598.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b68963a152bb8afd1639340ef0b654a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a9fa8832f98b5418a7d75892f7951b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edd0c00f62c22e90e7d542a2f8dd83d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae7a3e520a16d4fdd73c4e6a4ce7be0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/404728d0ea2699c71e674f30dd984abd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/4/623d18bc-3602-4449-aa84-9a8d5008eecb.png?resizew=165)
您最近一年使用:0次
名校
解题方法
3 . 如图,正方形和正方形
的边长都是1,且它们所在的平面所成的二面角
的大小是
,则直线
和
夹角的余弦值为
分别是
上的动点,且
,则
的最小值是
您最近一年使用:0次
2024-01-30更新
|
792次组卷
|
4卷引用:广东省广州市天河区2023-2024学年高二上学期期末数学试题
广东省广州市天河区2023-2024学年高二上学期期末数学试题江西省南昌市第二中学2024届高三“九省联考”考后适应性测试数学试题(四)(已下线)第二章 立体几何中的计算 专题七 空间范围与最值问题 微点1 线段、距离、周长的范围与最值问题(一)【基础版】(已下线)【类题归纳】 不垂模型 基底为王
解题方法
4 . 如图,二面角
的棱上有两个点
,线段
与
分别在这个二面角的两个面内,并且都垂直于棱
,若
,则二面角
的余弦值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754bbd99327195520a4ca3ce3b9a0577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433c152d40b488ce9828f9179207e52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754bbd99327195520a4ca3ce3b9a0577.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/11/50768106-b502-4750-b690-f18cc6c8b576.png?resizew=162)
您最近一年使用:0次
名校
解题方法
5 . 各棱长均为1且底面为正方形的平行六面体
,满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6660dbf8615c2a0dda71f6d9f395c1a5.png)
______ ;此平行六面体的体积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ecbca919bff5a39a99dd7f867dd61f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6660dbf8615c2a0dda71f6d9f395c1a5.png)
您最近一年使用:0次
2024-01-18更新
|
1177次组卷
|
5卷引用:广东省广州科学城中学2023-2024学年高一下学期期中检测数学试题
名校
解题方法
6 . 如图,在平行六面体
中,
,
,
,
,
.则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b2ebbdc180eb05041d2f40fa2a8277b.png)
____________ ;该平行六面体的体积为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa5600c2061f6e12991bf271a4a3ab51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6037bba27008abc96a6dba99753549ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fcf6a87fd2d2034aab93631a4a4ac5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b2ebbdc180eb05041d2f40fa2a8277b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/21/a08566c8-8c76-4a6a-9b26-0849e99c79f7.png?resizew=196)
您最近一年使用:0次
解题方法
7 . 已知点
在平面
内,从
出发的三条两两垂直的棱
,
,
都在平面
的同侧,若顶点
,
,
到平面
的距离分别为1,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9571c50001558db720aed03d5bee77a3.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/902f97913e1af1e6c793f7edfe6b2114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d4aca03910382accfe738520daf689c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9571c50001558db720aed03d5bee77a3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/19/92a36776-5ec9-45d2-aac0-0144cc7731bc.png?resizew=189)
您最近一年使用:0次
解题方法
8 . 如图,二面角
的棱上有两个点
,
,线段
与
分别在这个二面角两个面内,并且都垂直于棱
.若二面角
的平面角为
,且
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ec5d678ec42846e1d28301e3bfd4be.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754bbd99327195520a4ca3ce3b9a0577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754bbd99327195520a4ca3ce3b9a0577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1682d306c38087d9e6f7efb9cec596a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d71e6ea7333dbc78d0a7b9bc3892f940.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ec5d678ec42846e1d28301e3bfd4be.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/22/24ea2f61-09a1-4795-8a9b-e9994762f8cb.png?resizew=191)
您最近一年使用:0次
2023-11-21更新
|
360次组卷
|
3卷引用:广东省佛山市超盈实验中学2023-2024学年高二上学期第二次段考复习数学试题
9 . 平行六面体
中,
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25b59cd60e4ca6523867bb23b243eb8e.png)
______ ;若动点
在直线
上运动,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92105835f8075cb75dff244e908370b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be560befd3ac8e670f8b6edd15edf31d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25b59cd60e4ca6523867bb23b243eb8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e539f26ed5e0b20ff7220559324869a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab7aaa871ceb78e5b80b531a7cf4f1c9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/10/eacf1f87-0cbc-4241-bce4-54dbfc115d1f.png?resizew=173)
您最近一年使用:0次
2023-11-16更新
|
252次组卷
|
3卷引用:广东省东莞松山湖未来学校2023-2024学年高二上学期期中数学试题
广东省东莞松山湖未来学校2023-2024学年高二上学期期中数学试题广东省佛山市顺德区华侨中学2023-2024学年高二上学期12月月考数学试题(已下线)第3章 空间向量及其应用(知识归纳+题型突破)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第一册)
名校
10 . 如图在平行六面体
中,
,
,则
的长是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1293b8ae0b30ce957da6b41b102d776a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64759b2af7abaf8a7ed92d0587bcf29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c92b5799d12ea37de46d7c942ce7a9.png)
![](https://img.xkw.com/dksih/QBM/2023/11/10/3364827010023424/3364875485208576/STEM/1b75344a4cfe475bb00c5a6909e1ba76.png?resizew=189)
您最近一年使用:0次
2023-11-10更新
|
316次组卷
|
5卷引用:广东省深圳外国语学校(集团)龙华高中部2023-2024学年高二上学期期中数学试题
广东省深圳外国语学校(集团)龙华高中部2023-2024学年高二上学期期中数学试题广东省深圳市深圳外国语学校高中园2023-2024学年高二上学期学段(一)数学试题重庆市第八中学校2021-2022学年高一下学期第二次月考数学试题(已下线)突破1.1 空间向量及其运算(重难点突破)(已下线)第1讲 空间向量及其运算 (2)