Answer :

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


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