Using distance formula prove that the following points are collinear :

A(3, -5, 1), B(-1, 0, 8) and C(7, -10, -6)

Given: A(3, -5, 1), B(-1, 0, 8) and C(7, -10, -6)


To prove: Points A, B and C are collinear


Formula used:


Points A, B and C are collinear if AB + BC = AC or AB + AC = BC or AC + BC = AB


Distance between any two points (a, b, c) and (m, n, o) is given by,



Therefore,


Distance between A(3, -5, 1) and B(-1, 0, 8) is AB,







Distance between B(-1, 0, 8) and C(7, -10, -6) is BC,







Distance between A(3, -5, 1) and C(7, -10, -6) is AC,







Clearly,


AB + AC




= BC


Hence, A, B and C are collinear


3