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 . 已知向量
,
,分别求出满足下列条件的
,并给出几何直观解释:
(1)
,
;
(2)
,
;
(3)
.
![](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/854e16eb319ee454088f5b527cf6c4d5.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0c8a433917f4a520455a2f4d824a484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c65c70ca04b673926a8e0214e9417df1.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ee6fd735eee435213a30ae2845caa7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1d8bbd5f09a1f1a3356c8fb9165f7c.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79945ddc5278569eb2ca2ebfce2d354e.png)
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2023-10-09更新
|
64次组卷
|
5卷引用:北师大版(2019)必修第二册课本习题第二章5.3利用数量积计算长度与角度
北师大版(2019)必修第二册课本习题第二章5.3利用数量积计算长度与角度(已下线)专题04 向量的数量积(1)-《重难点题型·高分突破》(苏教版2019必修第二册)(已下线)专题04 向量的数量积(1)-《重难点题型·高分突破》(已下线)5.3 利用数量积计算长度与角度北师大版(2019)必修第二册课本例题5.3 利用数量积计算长度与角度
解题方法
3 . 如图所示,求出以下向量的数量积.
;
(2)
;
(3)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22df38348fd58f330784eea5dece178e.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c91530b37edc18ed6a5f7e115f0d7a.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd13ed8a00a0ebdb73bb09fd1e907c9b.png)
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21-22高二·全国·课后作业
解题方法
4 . 已知
,
,
是两两垂直的单位向量,求:
(1)
;
(2)
;
(3)
在
方向上的投影数量;
(4)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a92e6eba8dab638fd66831cd3a0b6d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/427fa45527d0ce469bfd060bf6f991f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/524594bf0942ed86f56fc1eee120a81a.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecce1ed933a1802df36b35805d6a144a.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54edbd0eecf362003dd616d0e3eb3c90.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fc9dc8ef7c5d23a2ff670448ea6d137.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b98386771bbcbdb72732c37633dff29.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefaeecad135de6e2a6386a814873264.png)
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21-22高一·湖南·课后作业
5 . 在
中,已知
,
,
,求:
(1)
在
方向上的投影;
(2)
在
方向上的投影.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/767986ce276caa4e4e8e4a5f67217037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9143d674c8cdd2815ba91546fe295fbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60afefb1676c9260f6f96e2462ac9279.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b680f91c4a693cc9ab2c23f2e9114ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1fe2d802f2b37e7db198c5a3c1df9a4.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1fe2d802f2b37e7db198c5a3c1df9a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1da92a2fc2ce861e82f7192fe4e648f.png)
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21-22高一·湖南·课后作业
6 . 已知点A(-1,1),B(1,2),C(-2,-1),D(3,4),求
在
方向上的投影.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9795e7f5cb9b366776c41d8f3f43942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ed9c2e9fabbfc63733bae8fa079d00.png)
您最近一年使用:0次
21-22高一·湖南·课后作业
7 . 在平面直角坐标系xOy内,已知模长为4的向量
与x轴、y轴正方向的夹角分别为
和
,求
在x轴、y轴正方向上的投影.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9795e7f5cb9b366776c41d8f3f43942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f785147690f83dcee0a0bc6c327e75a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67d01e61dc0042e67b5e8ec8e727c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9795e7f5cb9b366776c41d8f3f43942.png)
您最近一年使用:0次
20-21高一·全国·课后作业
解题方法
8 . 已知
,
,设
与
的夹角为
,求
的值,并图示其意义.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd18461fd9d77e6fa46a654f0ab540f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fcb3a08974ade5d1697c0bf4a6f223c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba3900dd0b33bbbd2275c67aeb3de66a.png)
您最近一年使用:0次
9 . 已知
,求
在
上的投影的数量.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27167daac76e46fa34bf7bb08d5f3932.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/969604545902c9a66549a4a44ec3a3c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ab17fd4247cdd710c363d5d3fbc5bd.png)
您最近一年使用:0次
2020-02-13更新
|
222次组卷
|
3卷引用:人教B版(2019) 必修第三册 逆袭之路 第八章 8.1 向量的数量积
人教B版(2019) 必修第三册 逆袭之路 第八章 8.1 向量的数量积(已下线)第八章 向量的数量积与三角恒等变换 8.1 向量的数量积 8.1.3 向量数量积的坐标运算人教B版(2019)必修第三册课本习题习题8-1
解题方法
10 . 已知
,
在
上的投影的数量是
,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e73ff0aae5425f4dd007350c05ba60cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/969604545902c9a66549a4a44ec3a3c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ab17fd4247cdd710c363d5d3fbc5bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fb134b2b48acc99213fff6ccfee65f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a560b8ff794c12dc8d194bcd2e3f3554.png)
您最近一年使用:0次
2020-02-13更新
|
242次组卷
|
3卷引用:人教B版(2019) 必修第三册 逆袭之路 第八章 8.1 向量的数量积
人教B版(2019) 必修第三册 逆袭之路 第八章 8.1 向量的数量积(已下线)第八章 向量的数量积与三角恒等变换 8.1 向量的数量积 8.1.3 向量数量积的坐标运算人教B版(2019)必修第三册课本习题习题8-1