1 . 判断题(正确的填“正确”,错误的填“错误”):
(1)平行向量就是共线向量.( )
(2)若向量
的模小于
的模,则
.( )
(3)质量、动量、功、加速度都是向量.( )
(4)若
与
共线,则A,B,C,D四点必在一条直线上.( )
(5)若向量
与
平行,则
与
的方向相同或相反.( )
(6)在
中,
.( )
(7)若向量
与
有共同的起点,则以
的终点为起点,以
的终点为终点的向量等于
.( )
(8)若
且
,当
,则一定有
与
共线.( )
(9)若
,则
或
.( )
(10)若
且
,则
.( )
(11)向量
在
方向上的投影是一个模等于
,方向与
相同或相反的向量. ( )
(12)
.( )
(1)平行向量就是共线向量.
(2)若向量
![](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/de12437ea8219e16092749a45858053a.png)
(3)质量、动量、功、加速度都是向量.
(4)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcb5d89b04570ceda2c29e11cb27a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc1070a28cb9cb8553c29747d1993b16.png)
(5)若向量
![](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/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
(6)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e71163a9fd0b7c3b86d1c7f3267bde28.png)
(7)若向量
![](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/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb667795acdfafa436ee35e152adbc4.png)
(8)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13e87088da41685cc8d433fbbe0e18d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177bac525befae1da05679bba3735d30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11aeda90bd9777fda412249a37fc7a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
(9)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5addd0c822fa3c5ac9c7db649f6682cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eab00d21b5a95621c6b6164dfb9e08b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afff2ac07ebf0f4b8b498db0e256a72d.png)
(10)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa8f7351f41cbfc74f99de51c752ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f6e8e539b10975174077d1fbf8d8099.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58fbeefcb60bff9eab8243d3b4931123.png)
(11)向量
![](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/69107a1f19902da9c610086e94c86daf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
(12)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7960dd509a123a8efe26a32e1f0ea396.png)
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解题方法
2 . 如图,某八角镂空窗的边框呈正八边形.已知正八边形
的边长为
,
、
为正八边形内的点(含边界),
在
上的投影向量为
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d17d4a6cf11cda87b3dfafaecdec683f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bad299e2782c072d27e1c54422cc8fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcb5d89b04570ceda2c29e11cb27a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5f5ffe0f9de49ccaeb400b92f11afcb.png)
A.![]() | B.![]() |
C.![]() ![]() | D.![]() |
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2023-08-01更新
|
644次组卷
|
11卷引用:宁夏吴忠市2022-2023学年高一下学期期末联合调研考试数学试题
宁夏吴忠市2022-2023学年高一下学期期末联合调研考试数学试题(已下线)第13讲 拓展一:平面向量综合问题-【帮课堂】(人教A版2019必修第二册)(已下线)6.2.4 向量的数量积10种常考题型归类(1)-高频考点通关与解题策略(人教A版2019必修第二册)(已下线)高一下学期期中复习选择题压轴题十七大题型专练(1)-举一反三系列(人教A版2019必修第二册)福建省厦门第二中学2023-2024学年高一下学期第一阶段考试数学试卷(已下线)6.2.4 向量的数量积——课后作业(提升版)(已下线)模块一 专题4 平面向量的数量积 B提升卷(人教B版)(已下线)模块一 专题5 平面向量的数量积 B提升卷(北师大版高一期中)(已下线)高一下学期期末复习选择题压轴题二十三大题型专练(1)-举一反三系列(人教A版2019必修第二册)(已下线)【一题多变】向量点积,投影降维(已下线)FHsx1225yl157
解题方法
3 . 在平面直角坐标系中,已知
,
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce0c92a72568d2cb1279be8be88ba408.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab341f0e3b4da32f90a9f8b63ab9b92d.png)
A.![]() ![]() |
B.当![]() ![]() ![]() ![]() |
C.![]() ![]() |
D.若![]() ![]() ![]() |
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解题方法
4 . 如图,
均为等腰直角三角形,
在线段
上,
,在扇形
中,
为
的中点,
为
上一动点,
为线段
上一动点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8345eade0a8c625a0eb05cb993e890e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fea5d278b2333aacbaee65117cd9eff1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf126cfed85fa9b7720ec6f7b0008dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bb3820bab977db734f4335e4fde720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bb3820bab977db734f4335e4fde720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/17/958937f4-5df9-4fa9-948c-d75618dcd033.png?resizew=159)
A.向量![]() ![]() ![]() |
B.向量![]() ![]() ![]() ![]() |
C.当![]() ![]() ![]() ![]() |
D.当![]() ![]() ![]() ![]() |
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5 . (1)计算
;
(2)已知单位向量
与向量
互相垂直,求向量
在向量
方向上的投影向量.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e33723b55fc520a954f5953fde32330c.png)
(2)已知单位向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e684c1f3eb8f35ea78b443be530830.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d108e523626be0b40be9b3543ce12524.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
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2023-05-02更新
|
336次组卷
|
2卷引用:广东省三校2022-2023学年高一下学期期中联考数学试题
名校
解题方法
6 . 已知
是坐标原点,
,
(1)求向量
在
方向上的投影向量的坐标和数量投影;
(2)若
,
,
,请判断C、D、E三点是否共线,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1483e8351f585ca23025ec0c46f0a6e.png)
(1)求向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fc9656d8286c4d6fa309d6ae347c89e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f605ec0729ce6d72237ad662a06862.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ba0ea537c4145d273b81ada981ee3d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4600168dd0570abb535b7c15af66ddf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b594e00f9aad4faf4907ec01f8112eb5.png)
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2023-04-27更新
|
797次组卷
|
2卷引用:上海市松江二中2022-2023学年高一下学期期中数学试题
名校
7 . 已知函数
满足
.向量
,
,
,记
在
方向上的向量为
,则当
最大时,
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd0d0a3814462a00d06fc32ff4ea4da9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a936dd1f21df4b02daac8e667e4d328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d3ce134a42f342277ff7b53f6b1324f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57205378a6b6d78bb711fab2ecb938b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0b19e69be46452425916a0fcb49c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26abac73b9cb1af5c5d8e8c2dd136bbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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8 . 下列说法正确的是( )
A.若![]() ![]() ![]() |
B.![]() ![]() |
C.![]() |
D.若![]() ![]() ![]() ![]() |
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2023-04-08更新
|
598次组卷
|
2卷引用:四川省成都市树德中学2022-2023学年高一下学期4月月考数学试题
名校
解题方法
9 . 已知三角形
,
、
、
,与
垂直的一个非零向量为
.
(1)求点
的坐标;
(2)求
与
夹角的余弦值;
(3)求向量
在向量
上投影的数量.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6c09b41032e4722c412c2e2427500a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/858edb9a2fe9bab726479ec89a0f72c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc579e544939ba6a84c0f6ac76308445.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/083a20abb668d4c26fe5039bd108b40a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20e8636a2a9c4b3d588a9d29f24ec0ff.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcb5d89b04570ceda2c29e11cb27a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89265cbe3abc6b966ce8967fead448b.png)
(3)求向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/083a20abb668d4c26fe5039bd108b40a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89265cbe3abc6b966ce8967fead448b.png)
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10 . 下列命题不正确的有( )
A.复数![]() ![]() |
B.若非零向量![]() ![]() ![]() |
C.在![]() ![]() ![]() |
D.底面是正多边形的棱锥是正棱锥 |
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