Question

已知向量a,b,且AB=a+2b,BC=-4a+5b,CD=6a-b(AB,BC,CD,a,b,c是向量),则一定共线的

Answer 1

AC = AB + BC = a+2b-4a+5b = -3a+7b

AD = AC + CD = -3a+7b+6a-b= 3a+6b = 3(a+2b)=3AB

所以A、B、D一定共线