If ` vec A O+ vec O B= vec B O+ vec O C` , prove that `A , B , C` are collinear points.

Explanation

It is given that,

`vec(AO)+vec(OB) = vec(BO)+vec(OC)`

`=>vec(AB) = vec(BC)`

Adding `vec(BC)` both sides,

`=> vec(AB)+vec(BC) = 2vec(BC)`

`=>vec(AC) = 2vec(BC)`

As, these two vectors pass from same point and are in same direction and one is double of other, it means

`A`,`B` and `C` are collinear.