问题 填空题
已知向量
a
=(x,y),
b
=(-1,2 ),且
a
+
b
=(1,3),则|
a
-2
b
|
等于______.
答案

∵向量

a
=(x,y),
b
=(-1,2 ),

a
+
b
=(x-1,y+2)

a
+
b
=(1,3),

∴(x-1,y+2))=(1,3)

∴x-1=1,y+2=3,

∴x=2,y=1,

a
=(2,1)

∴|

a
|=
5
,|
b
|=
5
a
b
=0,

∴|

a
-2
b
|=
a
2
-4
a
b
+4
b
2
=
25
=5,

故答案为:5

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