It is given that
A (2, 3, 4), B (-1, -2, 1) and C (5, 8, 7)
AB = – 3i – 5j – 3k
So the point on the line AB with A on the line
R = (2, 3, 4) + a (- 3, -5, -3)
Consider C = (2 – 3a, 3 – 5a, 4 – 3a)
So we get
(5, 8, 7) = (2 – 3a, 3 – 5a, 4 – 3a)
Here if a = -1 we get LHS = RHS
So the point C lies on the line joining AB
Therefore, the three points are collinear.