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file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image002.png第六章平面向量及其应用
6.1 平面向量的概念
课后篇巩固提升
file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image004.jpg基础巩固
1.有下列物理量:①质量;②速度;③力;④加速度;⑤路程;⑥功.其中,不是向量的个数是( )
A.1 B.2 C.3 D.4
答案C
解析因为速度、力和加速度既有大小,又有方向,所以它们是向量;而质量、路程和功只有大小,没有方向,所以它们不是向量,故不是向量的个数是3.
2.正n边形有n条边,它们对应的向量依次为a1,a2,a3,…,an,则这n个向量( )
A.都相等 B.都共线
C.都不共线 D.模都相等
答案D
解析因为是正n边形,所以n条边的边长都相等,即这n个向量的模都相等.
3.
file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image006.png
如图所示,在正三角形ABC中,P,Q,R分别是AB,BC,AC的中点,则与向量file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image008.png相等的向量是( )
A.file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image010.png
B.file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image012.png
C.file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image014.png
D.file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image016.png
答案B
解析向量相等要求模相等,方向相同,因此file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image018.png都是和file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image008.png相等的向量.
4.若|file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image020.png|=|file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image022.png|且file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image024.png,则四边形ABCD的形状为( )
A.平行四边形 B.矩形
C.菱形 D.等腰梯形
答案C
解析由file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image024.png知AB=CD且AB∥CD,即四边形ABCD为平行四边形.又因为|file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image020.png|=|file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image022.png|,所以四边形ABCD为菱形.
5.设点O是正方形ABCD的中心,则下列结论错误的是( )
A.file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image026.png B.file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image028.png
C.file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image030.png共线 D.file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image032.png
答案D
file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image034.jpg
解析如图,∵file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image036.png方向相同,长度相等,∴选项A正确;
∵B,O,D三点在一条直线上,
∴file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image028.png,选项B正确;
∵AB∥CD,∴file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image038.png共线,
∴选项C正确;
∵file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image040.png方向不同,
∴file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image042.png,∴选项D错误.
file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image044.jpg
6.如图,四边形ABCD,CEFG,CGHD都是全等的菱形,HE与CG相交于点M,则下列关系不一定成立的是( )
A.|file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image020.png|=|file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image046.png|
B.file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image048.png共线
C.file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image050.png共线
D.file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image052.png共线
答案C
解析依题意知,直线BD与EH不一定平行,因此file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image054.png不一定与file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image056.png共线,C项错误.
file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image058.jpg
7.如图,在△ABC中,∠ACB的平分线CD交AB于点D.若file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image060.png的模为2,file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image062.png的模为3,file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image022.png的模为1,则file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image064.png的模为 .
答案file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image066.png
file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image068.jpg
解析如图,延长CD,过点A作BC的平行线交CD的延长线于点E.
因为∠ACD=∠BCD=∠AED,
所以|file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image060.png|=|file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image070.png|.
因为△ADE∽△BDC,
所以file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image072.png,
故|file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image064.png|=file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image066.png.
8.
file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image074.jpg
如图所示,4×3的矩形(每个小方格都是单位正方形),在起点和终点都在小方格的顶点处的向量中,试问:
(1)与file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image020.png相等的向量共有几个?
(2)与file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image020.png平行且模为file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image076.png的向量共有几个?
(3)与file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image020.png方向相同且模为3file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image076.png的向量共有几个?
解(1)与向量file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image020.png相等的向量共有5个(不包括file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image020.png本身).
(2)与向量file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image020.png平行且模为file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image076.png的向量共有24个.
(3)与向量file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image020.png方向相同且模为3file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image076.png的向量共有2个.
file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image004.jpg能力提升
file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image078.jpg
1.如图,四边形ABCD和ABDE都是边长为1的菱形,已知下列说法:
①file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image080.png都是单位向量;
②file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image082.png;
③与file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image020.png相等的向量有3个;
④与file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image070.png共线的向量有3个;
⑤与向量file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image084.png大小相等、方向相反的向量为file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image086.png.
其中正确的是 .(填序号)
答案①②④⑤
解析①由两菱形的边长都为1,故①正确;②正确;③与file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image020.png相等的向量是file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image088.png,故③错误;④与file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image070.png共线的向量是file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image090.png,故④正确;⑤正确.
file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image092.jpg
2.已知在四边形ABCD中,file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image094.png,且|file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image020.png|=|file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image060.png|,tan D=file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image096.png,判断四边形ABCD的形状.
解∵在四边形ABCD中,file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image094.png,
∴AB | 
