名校
解题方法
1 . 已知正四面体
棱长为2,点
分别是
,
,
内切圆上的动点,现有下列四个命题:
①对于任意点
,都存在点
,使
;
②存在
,使直线
平面
;
③当
最小时,三棱锥
的体积为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0467b0675c3ecfb282cc88255284d3e1.png)
④当
最大时,顶点
到平面
的距离的最大值为
.
其中正确的有___________ .(填选正确的序号即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f7807638578edd712265463a7a5eab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
①对于任意点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c89d54457ad06f095a8643cf3c77923.png)
②存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5425108c557f0f21474c045334f97d9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85e39cbda9b51329928487a7462cb550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b9ffc9d4fbb08792f487b787c71c8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d919276bf6174bdf850673cd38284cda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0467b0675c3ecfb282cc88255284d3e1.png)
④当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b9ffc9d4fbb08792f487b787c71c8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56448a74c1b8430c425d79d626764f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/839c7616cd0d90265f4b2c9c021254fe.png)
其中正确的有
您最近一年使用:0次
2024-06-05更新
|
358次组卷
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2卷引用:辽宁省部分高中2023-2024学年高三下学期第三次模拟考试数学试题
2 . 如图,正方形
和矩形
所在的平面互相垂直.点
在正方形
及其内部运动,点
在矩形
及其内部运动.设
,给出下列四个结论:
,使
;
②存在点
,使
;
③到直线
和
的距离相等的点
有无数个;
④若
,则四面体
体积的最大值为
.
其中所有正确结论的序号是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef70144bea23fc8154301b246bf3ef14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91f1c40ebcc993a5778478154c124f0c.png)
②存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b9d4191b4dc51fddb22d1faf650c3b.png)
③到直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f138877b595987abf3397aab8f9895e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3019bf62527f7e614c49b803d7b59d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
其中所有正确结论的序号是
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3 . 设
是以定点
为球心半径为
的球面,
是一个固定平面,
到
的距离为
.设
是以点
为球心的球面,它与
外切并与
相切.令A为满足上述条件的球心
构成的集合.设平面
与
平行且在
上有A中的点.设
是平面
与
之间的距离.则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54f562eb3c2a45d65cba066d712825a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf9f50605db5d5f8f3a01ee8e474a112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c2d70c47444cb333ff8d68e36a52181.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf9f50605db5d5f8f3a01ee8e474a112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c2d70c47444cb333ff8d68e36a52181.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95b2d4d75dec1ac907231fa1ce4e459a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d32c36fe601a5d0c26e1bdb0f8f66366.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54f562eb3c2a45d65cba066d712825a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c2d70c47444cb333ff8d68e36a52181.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ebba6ed1add0fe647c0226614b9290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c2d70c47444cb333ff8d68e36a52181.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ebba6ed1add0fe647c0226614b9290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907e10e5b0927b534415bc6e23fd0841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ebba6ed1add0fe647c0226614b9290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c2d70c47444cb333ff8d68e36a52181.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907e10e5b0927b534415bc6e23fd0841.png)
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2024-02-23更新
|
610次组卷
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4卷引用:安徽省六校教育研究会2023-2024学年高三下学期下学期第二次素养测试(2月)数学试题
安徽省六校教育研究会2023-2024学年高三下学期下学期第二次素养测试(2月)数学试题(已下线)第5套 最新模拟重组精华卷5---模块一 各地期末考试精选汇编河南省南阳市西峡县第一高级中学2023-2024学年高二下学期第一次调研测试数学试卷(已下线)第3题 空间距离最值问题(压轴小题)
名校
4 . 在空间直角坐标系中,点P坐标可记为
:定义柱面坐标系,在柱面坐标系中,点P坐标可记为
.如图所示,空间直角坐标
与柱面坐标
之间的变换公式为:
,
,
.则在柱面坐标系中,点
与点
两点距离的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d594e1827f2d6d03295009b1ed75b3d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9913222c15a1a347b1a02f76ed54a782.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d594e1827f2d6d03295009b1ed75b3d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9913222c15a1a347b1a02f76ed54a782.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2640f8df813aa4916984fb30e90a9a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41995465f408e58668525745373aa7c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2abb31a34f7c99d6891453dd1d6e6ffd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c34ace65d315585e942d7194fc08582.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d57e7a83bdad98eb39cadf3362abc0a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/6/93eda1ce-cbf2-4ae0-96ce-06455567531a.png?resizew=138)
您最近一年使用:0次
5 . (6)已知空间中
两点,则
两点之间的距离公式为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c84a09595eabd6ae21a2e8faa7465c.png)
_______________
(7)在空间直角坐标系中,y轴上的点的坐标形式为___________
(8)向量加减法运算法则:加法三角形法则:首尾相连,首指向尾为和.
加法平行四边形法则:共起点的两边为邻边作平行四边形,共起点_________ 为和.
减法三角形:同起点,连终点,方向________ .
(9)共线向量基本定理:空间两个向量![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b172cf8d898883d82e973f28c3c3a3e.png)
共线的充要条件是存在唯一的实数
,使得__________ .通常把这个定理称为共线向量基本定理.
(10)数乘运算律:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294c0f85a47e8f5e004611af0bdd75a5.png)
_______________ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93a4ee3c424455ab04b1cf0acfb87d62.png)
____________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3557f7de9f773172e5cd05574e958cbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c84a09595eabd6ae21a2e8faa7465c.png)
(7)在空间直角坐标系中,y轴上的点的坐标形式为
(8)向量加减法运算法则:加法三角形法则:首尾相连,首指向尾为和.
加法平行四边形法则:共起点的两边为邻边作平行四边形,共起点
减法三角形:同起点,连终点,方向
(9)共线向量基本定理:空间两个向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b172cf8d898883d82e973f28c3c3a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4220bc106912baca47334a7b767cb851.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(10)数乘运算律:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294c0f85a47e8f5e004611af0bdd75a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93a4ee3c424455ab04b1cf0acfb87d62.png)
您最近一年使用:0次
6 . 思维辨析(对的写“正确”,错的写“错误”)
(1)在空间直角坐标系中,点
关于
轴的对称点是
.( )
(2)在空间直角坐标系中,点
关于
坐标平面的对称点为
.( )
(3)向量
的坐标与点
的坐标一致.( )
(4)对于三个不共面向量
,
,
,不存在实数组
使得
.( )
(1)在空间直角坐标系中,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06981fa9b88bb9a4cfe62e30c98397a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e17309f76ab5070d4a150244ffe7e9a.png)
(2)在空间直角坐标系中,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06981fa9b88bb9a4cfe62e30c98397a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ef1e8a88d934eca5399decc64fdbd43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b043d85d604b9352901763b63227a9db.png)
(3)向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7239b3f2d88c2e45e17e5de9ae1a332.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(4)对于三个不共面向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d344174267f996c7cefecfd6985d380.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2e900404ba71110c5861ced9634646f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67dbe2e19d8960789ec873b687998b58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c527db289c2e140007aa5bb703ba93a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2214b9542c54d07e7c72e130bd5f1c75.png)
您最近一年使用:0次
名校
7 . 正四面体
的棱长为4,中心为点
,则以
为球心,1为半径的球面上任意一点
与该正四面体各顶点间的距离的平方和:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a054185eada6a05e374c41cd74dba46a.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a054185eada6a05e374c41cd74dba46a.png)
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2023-05-27更新
|
864次组卷
|
3卷引用:湖北省襄阳市第四中学2023届高三下学期高考适应性考试数学试题
湖北省襄阳市第四中学2023届高三下学期高考适应性考试数学试题云南省2024届高三上学期新高考联考数学试题(已下线)第二章 立体几何中的计算 专题六 空间定值问题 微点1 立体几何中的定值问题综述及定长、定距问题【培优版】
名校
8 . 某同学参加课外航模兴趣小组活动,学习模型制作.将一张菱形铁片
进行翻折,菱形的边长为1,
,E是边
上一点,将
沿着DE翻折到
位置,使平面
面
,则点A与
之间距离最小值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d631f45bc652539853f236952afa5bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/549e807ed5636b783c51603d38337313.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28cc4fea4432e3c2b4a35e5c4d1498ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d70676406f26d339465fe3473c0c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
您最近一年使用:0次
解题方法
9 . 已知矩形
,
,过
作平面
,使得平面
,点
在
内,且
与
所成的角为
,则点
的轨迹为______ ,
长度的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d84499931abecd42f1de666fabb9789c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41902f9de0821124bd01d7c9eb53b42b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
您最近一年使用:0次
22-23高二下·上海浦东新·阶段练习
名校
10 . 如图,棱长为1的正方体上有两个动点分别从顶点A、C同时出发并做匀速直线运动,最后同时到达顶点B、D,则在运动的过程中,两个动点间的最小距离为_____________
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/19/cf485206-a2e9-434c-bdfe-d66a07c6564c.png?resizew=135)
您最近一年使用:0次