已知向量AB=a+5b; BC=-2a+8b CD=3(a-b)则哪三点共线?
问题描述:
已知向量AB=a+5b; BC=-2a+8b CD=3(a-b)则哪三点共线?
答
OB-OA=AB =a+5b (1)
OC-OB = BC = -2a+8b (2)
OD-OC = CD = 3(a-b) (3)
(2)+(3)
OD-OB = a+5b =AB
=> BD =AB
=> A,B,D 三点共线