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