2020-2021学年高中数学北师大版(2019)必修第二册第二章】

2.2 向量的减法

课后篇巩固提升

基础达标练

1.化简EG ????? ?EF ????? =( )

A.EG ?????

B.EF ?????

C.FG ?????

D.GF ????? 2.化简AB ????? +BD ?????? ?CD ????? =( )

A.AC ?????

B.0

C.BC ?????

D.DA ????? 3.若O ,A ,B 是平面上不共线的任意三点,则以下各式中成立的是( )

A.AB ????? =OA ????? +OB ?????

B.AB ????? =OB ????? ?OA ?????

C.AB ????? =-OB ????? +OA ?????

D.AB ????? =-OB ????? ?OA ?????

4.(多选)化简以下各式,结果为0的有( )

A.AB ????? +BC ????? +CA ?????

B.AB ????? ?AC ????? +BD ?????? ?CD ?????

C.OA ????? ?OD ?????? +AD ?????

D.NQ ?????? +QP ????? +MN ??????? ?MP ??????

5.如图,已知ABCDEF 是一正六边形,O 是它的中心,其中OA ????? =a ,OB ????? =b ,OC ????? =c ,则EF ????? 等于(

)

A.a +b

B.b -a

C.c -b

D.b -c

6.化简:AB ????? +DA ????? +BD

?????? ?BC ????? ?CA ????? = . 7.已知菱形ABCD 的边长为2,则向量AB ????? ?CB ????? +CD

????? 的模为 ,|AC ????? |的范围是 .

8.化简下列向量表达式:

(1)OM

?????? ?ON ?????? +MP ?????? ?NA ?????? ; (2)(AD ????? ?BM ?????? )+(BC

????? ?MC ?????? ). 能力提升练

1.(多选)(2019山东济南一中高一期中)下列说法中正确的是( )

A.若AB

????? =DC ????? ,则A ,B ,C ,D 四点构成一个平行四边形 B.若a ∥b ,b ∥c ,则a ∥c

C.互为相反向量的两个向量模相等

D.OC ????? ?OA ????? +CD ????? =AD ?????

2.(2020四川泸县第四中学高一月考)已知OA ????? =a ,OB ????? =b ,OC

????? =c ,OD ?????? =d ,且四边形ABCD 为平行四边形,则( )

A.a +b +c +d =0

B.a -b +c -d =0

C.a +b -c -d =0

D.a -b -c +d =0

3.如图所示,在梯形ABCD 中,AD ∥BC ,AC 与BD 交于O 点,则BA

????? ?BC ????? ?OA ????? +OD ?????? +DA ????? = .

4.若a ≠0,b ≠0,且|a |=|b |=|a -b |,则a 与a +b 所在直线的夹角是 .

5.已知非零向量a ,b 满足|a |=√7+1,|b |=√7-1,且|a -b |=4,则|a +b |= .

6.如图所示,BC ????? =a ,CD ????? =b ,DE ????? =c .

(1)用a ,b 表示DB ?????? ;

(2)用b ,c 表示EC ????? .

素养培优练

(多选)已知a ,b 为非零向量,则下列命题中是真命题的是(

) A.若|a |+|b |=|a +b |,则a 与b 方向相同

B.若|a |+|b |=|a -b |,则a 与b 方向相反

C.若|a |+|b |=|a -b |,则a 与b 有相等的模

D.若||a |-|b ||=|a -b |,则a 与b 方向相同

2.2 向量的减法

课后篇巩固提升

基础达标练

1.化简EG ????? ?EF ????? =( )

A.EG ?????

B.EF ?????

C.FG ?????

D.GF

????? 解析由平面向量减法三角形法则可知EG ????? ?EF ????? =FG

????? .故选C . 答案C

2.化简AB ????? +BD

?????? ?CD ????? =( ) A.AC ????? B.0 C.BC ????? D.DA ????? 解析AB

????? +BD ?????? ?CD ????? =AD ????? ?CD ????? =AD ????? +DC ????? =AC ????? .故选A . 答案A

3.若O ,A ,B 是平面上不共线的任意三点,则以下各式中成立的是( ) A.AB

????? =OA ????? +OB ????? B.AB ????? =OB ????? ?OA ????? C.AB ????? =-OB ????? +OA ????? D.AB

????? =-OB ????? ?OA ????? 解析由平面向量的线性运算可知,AB ????? =OB ????? ?OA ????? .故选B .

答案B

4.(多选)化简以下各式,结果为0的有( )

A.AB

????? +BC ????? +CA ????? B.AB ????? ?AC ????? +BD

?????? ?CD ????? C.OA ????? ?OD ?????? +AD ?????

D.NQ ?????? +QP ????? +MN

??????? ?MP ?????? 解析AB

????? +BC ????? +CA ????? =AC ????? +CA ????? =0; AB ????? ?AC ????? +BD ?????? ?CD ????? =CB ????? +BD

?????? ?CD ????? =CD ????? ?CD ????? =0; OA ????? ?OD ?????? +AD ????? =DA ????? +AD ????? =DA ????? ?DA ????? =0;

NQ ?????? +QP ????? +MN ??????? ?MP ?????? =NP ?????? +PN ?????? =NP ?????? ?NP ?????? =0.故选ABCD .

5.如图,已知ABCDEF 是一正六边形,O 是它的中心,其中OA ????? =a ,OB ????? =b ,OC ????? =c ,则EF

????? 等于( )

A.a +b

B.b -a

C.c -b

D.b -c

??? =OA ????? =CB

????? =OB ????? ?OC ????? =b -c .故选D .

6.化简:AB ????? +DA ????? +BD

?????? ?BC ????? ?CA ????? = .

=AB

????? +BD ?????? +DA ????? -(BC ????? +CA ????? )=0-BA ????? =AB ????? .

? 7.已知菱形ABCD 的边长为2,则向量AB

????? ?CB ????? +CD ????? 的模为 ,|AC ????? |的范围是 .

AB ????? ?CB ????? +CD ????? =AB ????? +BC ????? +CD ????? =AD ????? ,

又|AD ????? |=2,所以|AB ????? ?CB ????? +CD ????? |=|AD ????? |=2. 又因为AC ????? =AB ????? +AD ????? ,且在菱形ABCD 中,|AB ????? |=2, 所以||AB ????? |-|AD ????? ||<|AC ????? |=|AB ????? +AD ????? |<|AB ????? |+|AD ????? |,即0<|AC ????? |<4.

(0,4)

8.化简下列向量表达式: (1)OM ?????? ?ON ?????? +MP ?????? ?NA ?????? ;

(2)(AD ????? ?BM ?????? )+(BC

????? ?MC ?????? ).

OM ?????? ?ON ?????? +MP ?????? ?NA ?????? =NM ??????? +MP ?????? ?NA ?????? =NP

?????? ?NA ?????? =AP ????? . (2)(AD ????? ?BM ?????? )+(BC ????? ?MC ?????? )=AD ????? +MB ?????? +BC ????? +CM ?????? =AD ????? +(MB ?????? +BC ????? +CM ?????? )=AD ????? +0=AD ????? .

能力提升练

1.(多选)(2019山东济南一中高一期中)下列说法中正确的是( )

A.若AB

????? =DC ????? ,则A ,B ,C ,D 四点构成一个平行四边形 B.若a ∥b ,b ∥c ,则a ∥c

C.互为相反向量的两个向量模相等

D.OC ????? ?OA ????? +CD ????? =AD ?????

A ,

B ,

C ,

D 四点共线时,不成立,故A 错误;零向量与任何向量共线,当b =0时,a ∥b ,b ∥c ,则a

∥c 不成立,故B 错误;互为相反向量的模相等,方向相反,故C 正确;OC ????? ?OA ????? +CD ????? =AC ????? +CD

????? =AD ????? ,故D 正确;故选CD .

2.(2020四川泸县第四中学高一月考)已知OA ????? =a ,OB ????? =b ,OC

????? =c ,OD ?????? =d ,且四边形ABCD 为平行四边形,则( )

A.a +b +c +d =0

B.a -b +c -d =0

C.a +b -c -d =0

D.a -b -c +d =0

OB

????? ?OA ????? =AB ????? ,OC ????? ?OD ?????? =DC ????? ,而在平行四边形ABCD 中,AB ????? =DC ????? ,所以OB ????? ?OA ????? =OC

????? ?OD ?????? ,即b -a =c -d ,也即a -b +c -d =0.故选B .

3.如图所示,在梯形ABCD 中,AD ∥B …… 此处隐藏：4293字，全部文档内容请下载后查看。喜欢就下载吧 ……