名校
解题方法
1 . 已知平面向量
均为单位向量,且夹角为
,若向量
共面,且满足
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e8b95a61af300412fc65f846089028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/972aa316d122d8558ad4c35d124e5cf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c085cdf76f6027dd63e98f778637cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/498e31243c96cee074159c14530ce929.png)
A.![]() | B.![]() | C.![]() | D.2 |
您最近一年使用:0次
名校
解题方法
2 . 已知
是平面内任意两个非零不共线向量,过平面内任一点
作
,
,以
为原点,分别以射线
为
轴的正半轴,建立平面坐标系,如左图.我们把这个由基底
确定的坐标系
称为基底
坐标系
.当向量
不垂直时,坐标系
就是平面斜坐标系,简记为
.对平面内任一点
,连结
,由平面向量基本定理可知,存在唯一实数对
,使得
,则称实数对
为点
在斜坐标系
中的坐标.
(长度单位为米,如右图),且
,设![](https://staticzujuan.xkw.com/quesimg/Upload/formula/685535354ea99d84fd8e59e5bb509483.png)
(1)计算
的大小;
(2)质点甲在
上距
点4米的点
处,质点乙在
上距
点1米的点
处,现在甲沿
的方向,乙沿
的方向同时以3米/小时的速度移动.
①若过2小时后质点甲到达
点,质点乙到达
点,请用
,表示
;
②若
时刻,质点甲到达
点,质点乙到达
点,求两质点何时相距最短,并求出最短距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a076848a8ffbd0760fcdfd36b8ae8437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8114aa9f42de32336bfab841980d8a24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4181d61c3ce87141eeb3433c872529a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc7553e6eb48e82ed03fab82d9d3f591.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2e647c14561826ba9e396acc5a3792c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d4833bdfaf0e3c186c3748699aaedee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59fc0767aa413e427b60d09c84e3615.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d4833bdfaf0e3c186c3748699aaedee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9851846d24701bf7ab3b35fce7676d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4647b85ebbbc8889720c6ff3c929cd66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecbed7a9a503f5897311840eec49e940.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4647b85ebbbc8889720c6ff3c929cd66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a314ab1aa622c7962cdfdee02410203e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53147d334931501aa2a1140e00ceeca3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d62eeab1830414dbbff26e27c6c78436.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/685535354ea99d84fd8e59e5bb509483.png)
(1)计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88b14123852c3e17f0a519282e076797.png)
(2)质点甲在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e5af20b2f8c1fba4470f9650989e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b14069d21d32c724f0ebe3e311f114c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167f121a878699fa60e6cb467bf10484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/320319d8230188d5fd7e7c7f4a540ae1.png)
①若过2小时后质点甲到达
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af62a51e61a58e7fb5ff757d34695ca3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc1070a28cb9cb8553c29747d1993b16.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
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2024-04-07更新
|
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|
15卷引用:重庆市渝东九校联盟2022-2023学年高一下学期期中数学试题
重庆市渝东九校联盟2022-2023学年高一下学期期中数学试题重庆市荣昌中学校2023-2024学年高一下学期3月月考数学试题(已下线)单元提升卷07 平面向量与复数(已下线)模块一 专题2 平面向量基本定理与坐标运算(B)广东省东莞市众美中学2023-2024学年高一下学期3月月考数学试题广东省东莞市海德双语学校2023-2024学年高一下学期第一次月考数学试题(已下线)模块一专题2 《平面向量基本定理与坐标运算》B提升卷(苏教版)(已下线)模块三 专题2 解答题分类练 专题5 三角函数与平面向量的实际应用(解答题)(北师大版高一期中)(已下线)模块一 专题4 平面向量基本定理与坐标运算(B)北师大版高一期中安徽省合肥市普通高中六校联盟2023-2024学年高一下学期4月期中联考数学试题(已下线)高一第二学期第三次月考(范围:第9~14章)-重难点突破及混淆易错规避(苏教版2019必修第二册)广东省麻涌,塘厦,七中,济川四校2023-2024学年高一下学期5月期中联考数学试题辽宁省实验中学2023-2024学年高一下学期期中阶段测试数学试卷广东省深圳市龙岗区平湖外国语学校2023-2024学年高一下学期期中考试数学试题安徽省马鞍山二中2024年高一6月月考数学试题
名校
解题方法
3 . 已知边长为
的等边
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/105ec23be7d6a51641b0d2c4aace9bee.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fea78417d91d06cf20a16778b337f38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/105ec23be7d6a51641b0d2c4aace9bee.png)
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2024-03-23更新
|
429次组卷
|
3卷引用:重庆市中山外国语学校2022-2023学年高一下学期5月月考数学试卷
名校
解题方法
4 . 已知向量
满足
,
,则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23c5d7ba714351d679bbbb287af5aaec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eed4224248fe3bbc348eda59425fd726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98fe6c406e1d1b1007eb3876687a5d7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4051a3d29e6910a9272f0e04d350f88c.png)
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解题方法
5 . 已知向量
,
,
,
,
与
的夹角为120°,若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02af59613596682734297aebc578801.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e405db6c09d6ab5739cabbb63cd3b3bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4048243b09dfcfe2f7d1e43ccc4e3441.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-08-27更新
|
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|
8卷引用:重庆市永川双石中学校2024届高三上学期半期考试(期中)数学试题
名校
解题方法
6 . 已知
是
的重心,
是空间中的一点,满足
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eded1297a93002f3f5c4d0cdd9577ba9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c76263056b7ff5fb421401a5e23919e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53dc167055c0bdbd78061b6c062b35f1.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-01-05更新
|
1035次组卷
|
3卷引用:重庆市第十八中学2023-2024学年高二上学期期末模拟数学试题(A卷)
名校
7 . 已知点
,动点P满足
,设P的轨迹为C.
(1)求C的轨迹方程;
(2)若过点A的直线与C交于M,N两点,求
取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8b3f3c6e7712b32b861739dc84b004c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d3dc79197932c3d12db7e42ecd9f309.png)
(1)求C的轨迹方程;
(2)若过点A的直线与C交于M,N两点,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43edc7cf4e4ca28b7125ca4ba1fa7add.png)
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8 . 如图,在边长为2的等边三角形
中,点
为中线
的三等分点
靠近点
,点
为
的中点,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce08128582a7e855852c03e0ac5d0487.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5a1f589137c01b1dade3db58b9d0445.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aac2d928075fb4efcc731bbdd0ee6e15.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
9 . 单位向量
相互垂直,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98e85191a402d66a6ce28532710a24d8.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e8b95a61af300412fc65f846089028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98e85191a402d66a6ce28532710a24d8.png)
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解题方法
10 . 已知
,
,
与
的夹角是
.则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0df8996d500c3385a20a45d3ce469cc5.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/787379f7ff8d24be7eebfea1cfe956d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa56939ec2eced74373148ca41a99a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c0927afc571a7c966c98192040979e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0df8996d500c3385a20a45d3ce469cc5.png)
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