Given: A(4, -3, -1), B(5, -7, 6) and C(3, 1, -8)

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

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

Therefore,

Distance between A(4, -3, -1) and B(5, -7, 6) is AB,

Distance between B(5, -7, 6) and C(3, 1, -8) is BC,

Distance between A(4, -3, -1) and C(3, 1, -8) is AC,

Clearly,

AB + AC

= BC

Hence, A, B and C are collinear