Question

Help please... show that A,B,C are collinear
OA=(4,14,-5) OB=(1,2,7) OC= (2,6,3)

Answer 1

If A,B,C are collinear, unit vectors of AB and BC should be equal (identical), or
AB=k*BC where k \(\in\)R.
AB=<1-4,2-14,7-(-5))=<-3,-12,12>
BC=<2-1,6-2,3-7)=<1,4,-4>
I'll leave you to do the second part AB=k*BC.

Answer 2

collinear means "lie on the same line"
I would show all 3 points lie on the line
P= (1,2,7)+ t*(1,4,-4)