If ABC three points are collinear, what is the relationship between vector OA, vector OB and vector OC
I've omitted the word vector here
OB=λOA+μOC=(1-μ)OA+μOC=OA+μ(OC-OB)=OA+μBC
So ob-oa = μ BC
That is ab = μ BC
And AB and BC have a common point B
So ABC three points are collinear