1 . 已知
分别是与x轴,y轴正方向相同的单位向量,
,对任意正整数n,
.
(1)若
,求a的值;
(2)求向量
;
(3)记
,若不等式
恒成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0d0f5edd2ad69fa56e7782b85bba717.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0fd4ce43685ca97ee2816f6312a5232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd2808f6a2f014dcc6833a6f23f704f3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef973011d4954d469d4fb1b006feb2e1.png)
(2)求向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cae8824ce99db6c44633cc81b2c4257d.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed2938bdc6bcb2e3cd8d6510263d8dda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79672ffe0b0627b99daa3d4f5984d4b.png)
您最近一年使用:0次
2 . 计算:
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed31ae693bc3c034dda06045893c693f.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dea2f03e8dc815f81492a4437c996f8.png)
您最近一年使用:0次
2022-08-22更新
|
1693次组卷
|
14卷引用:广东省佛山市南海区南海执信中学2022-2023学年高二上学期开学考试数学试题
广东省佛山市南海区南海执信中学2022-2023学年高二上学期开学考试数学试题苏教版(2019) 必修第二册 一课一练 第9章 平面向量 9.2 向量运算 第3课时 向量的数乘(已下线)第01讲 平面向量的概念及其线性运算 (高频考点—精练)(已下线)6.2.3 向量的数乘运算1-2022-2023学年高一数学《考点·题型·技巧》精讲与精练高分突破系列(人教A版2019必修第二册)(已下线)6.2.3向量的数乘运算(分层作业)-【上好课】2022-2023学年高一数学同步备课系列(人教A版2019必修第二册)(已下线)9.2.2 向量的数乘1陕西省西安市第六中学“名校+”教育联合体2022-2023学年高一下学期第一次考练数学试题(已下线)专题6.4 平面向量的运算(重难点题型检测)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)(已下线)6.2.3 向量的数乘运算-高一数学同步精品课堂(人教A版2019必修第二册)(已下线)专题02 平面向量的运算(题型专练)-2《知识解读·题型专练》(人教A版2019必修第二册)(已下线)专题03 向量的数乘(1)-《重难点题型·高分突破》(苏教版2019必修第二册)(已下线)专题9.2 向量的加减及数乘运算-重难点突破及混淆易错规避(苏教版2019必修第二册)(已下线)9.2 向量运算1-【帮课堂】(苏教版2019必修第二册)(已下线)专题03 向量的数乘运算(1)-《重难点题型·高分突破》
名校
解题方法
3 . 如图,在△AOB中,已知|
|= 2,|
| = 2
,∠AOB = 90°,单位圆O与OA交于C,
= λ
,λ
(0,1),P为单位圆O上的动点.
+
=
,求λ的值;
(2)记|
|的最小值为f(λ),求f(λ)的表达式及f(λ)的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d60dcb171bb7fd972aab8294d63acdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f68628a408537b1cf3bf1ca2a69731b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bd98a891fa65f2fc6688001b03185d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9795e7f5cb9b366776c41d8f3f43942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6709005381938ae7f06aeb3df0a4e9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d20ec3efaa6b6ff5769e8999df5714a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cec64476aaca08de0808afda3618109c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0762365cf0afd8d6966d7d3407e2ade0.png)
(2)记|
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ae40c0f4bbc712cb3be8479243a434.png)
您最近一年使用:0次
2021-07-15更新
|
461次组卷
|
4卷引用:江西省宜春市上高二中2021-2022学年高一4月第七次月考数学试题
名校
4 . 如图,在正
中,
,
,
分别是
、
边上一点,并且
,设
,
与
相交于
.
,
表示
;
(2)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54bb101a25e7778ce31cf54520084035.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41a21451778eb1227a949c4dbb6700da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9795e7f5cb9b366776c41d8f3f43942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be64d59ac6538a0f4d79fb825e082081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68f654198c1e01d97f1378b35d7c68ca.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e8da00516e174f59162550688530fce.png)
您最近一年使用:0次
2020-09-23更新
|
702次组卷
|
4卷引用:上海市上海师范大学附属中学2020-2021学年高二上学期期中数学试题
上海市上海师范大学附属中学2020-2021学年高二上学期期中数学试题上海市南洋模范中学2020-2021学年高二上学期12月月考数学试题湖北省武汉市部分重点中学(武汉六中等)2019-2020学年高一(下)期末数学试题(已下线)专题24 平面向量的几何运算与坐标运算-备战2022年高考数学一轮复习一网打尽之重点难点突破
5 . 在复平面内,复数-3-i与5+i对应的向量分别是
与
,其中O是原点,求向量
+
,
对应的复数及A,B两点间的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/651d15ba8eeb38125c8a9a5190608c9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd7d2c9c617deec0cc6ab06af5d01be2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/651d15ba8eeb38125c8a9a5190608c9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd7d2c9c617deec0cc6ab06af5d01be2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305d5f36a9fdbc840161b36563923195.png)
您最近一年使用:0次
2020-04-06更新
|
299次组卷
|
3卷引用:2019年4月11日 《每日一题》理数选修2-2(期中复习)-数系的扩充和复数的概念
(已下线)2019年4月11日 《每日一题》理数选修2-2(期中复习)-数系的扩充和复数的概念专题07 复数的概念及运算(核心素养练习)-【新教材精创】2019-2020高一数学新教材知识讲学(人教A版必修第二册)-《高中新教材知识讲学》北师大版(2019) 必修第二册 金榜题名 第五章 复数 §2 复数的四则运算 2.1 复数的加法与减法
6 . 在直角坐标平面内,已知
,其中
为正整数,对于平面上任意一点
,记
为
关于
的对称点,
为
关于
的对称点,…
为
关于
的对称点.
(1)求向量
的坐标;
(2)对于任意偶数
,用
表示向量
的坐标;
(3)当点
在函数
图像上移动时,点
形成的是函数
的图像,其中
是以3为周期的周期函数,且当
时,
,求:函数
在
上的解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f47f34cde5bbfb39cb6daf0db92f90a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94ea50db79b18d8700cfa2559ff5e2d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
(1)求向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12787674cf0f0e71eec9ac3d1727fda4.png)
(2)对于任意偶数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dc801f5007dec6cf5183bfd3051fb02.png)
(3)当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b2428921c82d2ace53ade031fa21fea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f0499141930680241c2d8fc5bd1922c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f837c94d95e0c7bedc3b49c414a95cb2.png)
您最近一年使用:0次
7 . 已知平行四边形
中,若
是该平面上任意一点,则满足
(
).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/e37bff09-0338-46ea-9759-17c509c118ee.png?resizew=194)
(1)若
是
的中点,求
的值;
(2)若
、
、
三点共线,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac8f76a25cff46e6dce21b266a3363b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa72c594ebe33496fa7b9edf1db5c7e1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/e37bff09-0338-46ea-9759-17c509c118ee.png?resizew=194)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
(2)若
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6096acdd2d0ce16e1e45397ec5e365d4.png)
您最近一年使用:0次
8 . 设x轴、y轴正方向上的单位向量分别是
、
,坐标平面上点列
分别满足下列两个条件:①
且
;②
且
;
(1)写出
及
的坐标;
(2)求
的坐标;
(3)若△
的面积是
,求
的表达式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc1480988d26abda64d9a4d20674ab76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89cdb00326a922074494892c166aeefe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6ae2df3cfe81200ae0bf898612c93cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d37882749aa24648a00cbf1b6ac504.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ba11c64701e24d76699ce3540b0de76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79dcb1c9ae679a2c9d39cbe3aef4026e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acdb889e41dc848490eeea1974a47650.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7179a1cec8c930d7c6afcaee2c4d908f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/badbf0073031a679eb0caa32f42600ef.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/099448be5ba5b5ed61a197916a6bd8b4.png)
(3)若△
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1358519202b1299715f79cf147e6436a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4560c3ab498f2b5aaef05df664315703.png)
您最近一年使用:0次
9 . 设不共线的两个向量
,
,若
,
,
.求证:
、
、
三点共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8315ec34019d719771152be2252106e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf39ca3294f5520518dd4f1c0609876.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75fc4ac16a4fd56a609a93cf3e3914ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93bd143522ba26604b45345b6b8c9e8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061ab59acb9b114ddd8bdaf13bff7cb6.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/8455657dde27aabe6adb7b188e031c11.png)
您最近一年使用:0次
2019-11-10更新
|
245次组卷
|
4卷引用:沪教版 高二年级第一学期 领航者 第八章 附录3 实数与向量的乘积
10 . 正六边形
中,
是其中心,设
,
,用
、
表示
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44f957651ccff367a9275f258e923f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91407b166dc4b3f012543332dd19bad3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9856ad2a8dd1b673ec2cfa9ee0a1eaff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/184c6736108865aa9ba3680f3d50526a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d036188ce294e3c7427d0b7d2294fd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d86ed5700cde027ca83174d9c10292.png)
您最近一年使用:0次
2019-11-10更新
|
125次组卷
|
3卷引用:沪教版 高二年级第一学期 领航者 第八章 附录3 实数与向量的乘积