1 . 向量集合
,对于任意
,以及任意
,都有
,则称
为“
类集”,现有四个命题:
①若
为“
类集”,则集合
也是“
类集”;
②若
,
都是“
类集”,则集合
也是“
类集”;
③若
都是“
类集”,则
也是“
类集”;
④若
都是“
类集”,且交集非空,则
也是“
类集”.
其中正确的命题有________ (填所有正确命题的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f2c0b5b15ef55baeb6e7095ce47d5c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eea4b13fe0b06f86baad673fa423037e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eb6bf23a5a12e1ba5413594d7b1a57c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5913b03e244adcf4dec8749f9624d55f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59b4ea32d1f3ed0e04bcedca9f189941.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/148db9c7b8abbeaa814e8083bcd01c80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2646f41226f24960a6186dc7860ef45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b76d26b78e63683dfacf10d3da6d74d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
其中正确的命题有
您最近一年使用:0次
2020-02-29更新
|
1464次组卷
|
12卷引用:上海市华东师范大学第二附属中学2022-2023学年高二上学期开学考试数学试题
(已下线)上海市华东师范大学第二附属中学2022-2023学年高二上学期开学考试数学试题(已下线)第3章 空间向量及其应用(压轴题专练)-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)2020届上海市杨浦区高三第一次模拟(期末)数学试题2020届上海市高三高考压轴卷数学试题(已下线)专题10 集合与命题新定义-2020年高考数学母题题源全揭秘(浙江专版)(已下线)热点01 集合与逻辑-2021年高考数学【热点·重点·难点】专练(上海专用)(已下线)卷11-【赢在高考·黄金20卷】备战2021高考数学全真模拟卷(北京专用)(已下线)第01讲 集合与逻辑-2(已下线)高一上学期第一次月考填空题压轴题50题专练-举一反三系列(已下线)压轴题平面向量与解三角形新定义题(九省联考第19题模式)练(已下线)北京市中国人民大学附属中学2023-2024学年高一下学期期中练习数学试题变式题11-15(已下线)【练】专题四 与平面向量有关的新定义问题(压轴大全)
名校
解题方法
2 . 记
,设
,
为平面内的非零向量,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d4f30f140dedbe537c7bc2ec17cd8f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/969604545902c9a66549a4a44ec3a3c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ab17fd4247cdd710c363d5d3fbc5bd.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2020-02-14更新
|
967次组卷
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5卷引用:上海市复旦大学附属中学2016-2017学年高二上学期期中数学试题
上海市复旦大学附属中学2016-2017学年高二上学期期中数学试题(已下线)专题17 数学中的新定义问题-2021年高考冲刺之二轮专题精讲精析浙江省金华第一中学2021-2022学年高一下学期期中数学试题(已下线)重难点01平面向量的实际应用与新定义(3)(已下线)【练】专题四 与平面向量有关的新定义问题(压轴大全)
名校
解题方法
3 . 对于一个向量组
,令
,如果存在
,使得
,那么称
是该向量组的“长向量”
(1)若
是向量组
的“长向量”,且
,求实数
的取值范围;
(2)已知
,
,
均是向量组
的“长向量”,试探究
,
,
的等量关系并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d9c4e13c48813cb746b75ac8b842886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a589d1b2b9d250c545d81abd0282699a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c2dac5a1e64f5297958618920ffcd70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/752ed927125e4a75ae7c007db9c59683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b71760f71b439f7d3cba6429f1bc4cfa.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cde8b12aa232eeccc1e7ad1cc6d417c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a881c7a0b386a6fd3f43453a66197c28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07fbcd094482826c8759e06d899c7d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d970a4c8abf3fe4da3382206086a6cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2bc63bd663aed17c3b584ec105b7b18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cde8b12aa232eeccc1e7ad1cc6d417c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a881c7a0b386a6fd3f43453a66197c28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d970a4c8abf3fe4da3382206086a6cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2bc63bd663aed17c3b584ec105b7b18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cde8b12aa232eeccc1e7ad1cc6d417c1.png)
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16-17高二上·上海浦东新·阶段练习
名校
4 . 在平行四边形
中,过点C的直线与线段
、
分别相交于点M、N,若
,
;
(1)求y关于x的函数解析式;
(2)定义函数
(
),点列
(
,
)在函数
的图像上,且数列
是以1为首项,0.5为公比的等比数列,O为原点,令
,是否存在点
,使得
?若存在,求出Q点的坐标,若不存在,说明理由;
(3)设函数
为
上的偶函数,当
时,
,又函数
的图像关于直线
对称,当方程
在
(
)上有两个不同的实数解时,求实数a的取值范围;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a40ee38c74eeab2ab1d3760d275b59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/118f9aa8deddeed538d600bac65ee1d8.png)
(1)求y关于x的函数解析式;
(2)定义函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d16745051a2be22b6f1b9f2937ad5c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f5c837522a811402efb9762210c5362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a47e32fc61120ab08fe1fc65dc23bd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12b0e3b00fe47801afb53ec56706c21a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f5a90aeba435af22d6bcdb7b91650b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91587145b08f345881ad7ad1ed5de2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4e45596de995ef022f0bbe9818d8ba6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/832f15b6121d2d3001905865109d5bef.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89e593828316139a54019e352dec883f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c831aeeb8b6a466f06fffcf49b91a6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89e593828316139a54019e352dec883f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82bab8c444ffe566c8bb0f9ab8c18a36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/730368dee72935acc485d2a90bb5338e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ff2aa68223dfc02f39d7d10fa005387.png)
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15-16高二上·上海浦东新·期中
名校
5 . 对于向量
,把能够使得
取到最小值的点
称为
的“平衡点”.如图,矩形
的两条对角线相交于点
,延长
至
,使得
,联结
,分别交
于
两点.下列的结论中,正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/c435ac0b-3673-4c4c-94fa-e539a27a5a7d.png?resizew=190)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a56edad216aeb22b2d5cba7dfd4cb0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e22887f46e518331dcbd912a6a55ef3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee97c81587bdcf9158b37127923d3474.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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddc7897e3f49075943704f4dbef82e5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb9b29668bafeccf32ca33022e96d16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cf33d73483c93f24cc6a1d76ef22ca6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/c435ac0b-3673-4c4c-94fa-e539a27a5a7d.png?resizew=190)
A.![]() ![]() |
B.![]() ![]() |
C.![]() |
D.![]() ![]() |
您最近一年使用:0次