问题 选择题
设x,y∈R,向量
a
=(x,1),
b
=(1,y),
c
=(2,-4)且
a
c
b
c
,则|
a
+
b
|=(  )
A.
5
B.
10
C.2
5
D.10
答案

∵向量

a
=(x,1),
b
=(1,y),
c
=(2,-4)且
a
c
b
c
,则有2x-4=0,-4-2y=0,

解得 x=2,y=-2,故

a
+
b
=(3,-1 ).

故有|

a
+
b
|=
9+1
=
10

故选B.

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