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
|
370次组卷
|
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
名校
解题方法
2 . 正方体
的棱长为
,
是正方体表面及其内部一点,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
A.若![]() ![]() ![]() |
B.若![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() |
您最近一年使用:0次
解题方法
3 . 如图,
是矩形
所在平面外一点,
,二面角![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
为
,
为
中点,
为
中点,
为
中点.则下列说法正确的是( )
![](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/93b9239263f68a3c495a2b443fcedf7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27f35abf35a6045f10dd7f681fea6fee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
A.![]() | B.![]() ![]() |
C.![]() | D.![]() ![]() ![]() |
您最近一年使用:0次
4 . 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
您最近一年使用:0次
5 . 在空间直角坐标系Oxyz中,
,
,若直线AB与平面xOy交于点
,点P的轨迹方程为
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6377767f356676a837aff1b90ef3749c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c231fdd1209eca78428f4b2fd803c31e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7836750ff40c856e6aeb9ce0e239895.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad86ba09055ed2abe5b4299463b7b74b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88bee8e70f1fab639be1636c7bce0477.png)
A.1 | B.![]() | C.2 | D.![]() |
您最近一年使用:0次
名校
6 . 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)
您最近一年使用:0次
2024-01-20更新
|
148次组卷
|
2卷引用:上海市育才中学2023-2024学年高二上学期期末考试数学试卷
7 . (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)
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解题方法
8 . 在如图所示的结构对称的实验装置中,底面框架
是边长为2的正方形,两等腰三角形框架
的腰长均为
,
框架
所在的平面,
,活动弹子
分别在
上移动,
之间用有弹性的细线连接,且
始终成立,则当
的长度取得最小值时,
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a88913c44aff5636afe9beef5778075a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4901a7eda97d6a307db76c4fb196ba3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee47ffb34594a331ae59f16e63c2e9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/397c35711aa158529633c609101b4af1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac513f3836c413aba03eccdad2bd3ab3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/9/fff0e9b5-0ee9-465a-b2c5-7a839ea39dc4.png?resizew=168)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-11-15更新
|
206次组卷
|
2卷引用:安徽省“皖中联考”2023-2024学年高二上学期期中质检数学试题
9 . 回顾解析几何解决问题的思路,写出空间两点间距离的计算步骤.
您最近一年使用:0次
10 . 空间中,已知点
,点
在
轴上,则下列选项正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ceb02188683ddadd9232d4b98b3e10bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
A.若![]() ![]() | B.若![]() ![]() |
C.若![]() ![]() | D.若![]() ![]() |
您最近一年使用:0次