设OA=(-2,m),OB=(n,1),OC=(5,-1),若A、B、C三点共线,且OA⊥OB,则m+n的值是_.

问题描述:

OA
=(-2,m),
OB
=(n,1),
OC
=(5,-1),若A、B、C三点共线,且
OA
OB
,则m+n的值是______.

OA
=(-2,m),
OB
=(n,1),
OC
=(5,-1),
A、B、C三点共线,且
OA
OB

∴-2n+m=0,解得m=2n,
m+1
−2−5
=
2
n−5

解得n=3,m=6或n=
3
2
,m=3.
∴m+n=9或m+n=
9
2

故答案为:9或
9
2