Question

如果向量OA=(1,3),向量OB=(-3,5),C为AB的中点,那么向量OC=

Answer 1

OC=(OA+OB)/2

=((1,3)+(-3,5))/2

=(-2,8)/2

=(-1,4)

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令OC=(x,y)

AC=OC-OA=(x,y)-(1,3)=(x-1,y-3)

CB=OB-OC=(-3,5)-(x,y)=(-3-x,5-y)

C是AB中点,即：AC=CB

即：(x-1,y-3)=(-3-x,5-y)

即：x-1=-3-x,y-3=5-y

即：x=-1,y=4

即：OC=(-1,4)