We have to show that the three points are colinear , i.e. they all lie on the same line,

If we define a line which is having a parallel line to AB and the points A and B lie on it, if point C also satisfies the line then, the three points are colinear,

Given A(2, 3, 4) and B(-1, -2, 1), AB = -3i – 5j -3k

The points on the line AB with A on the line can be written as,

R = (2, 3, 4) +a(-3, -5, -3)

Let C = (2-3a, 3-5a, 4-3a)

ð (5, 8, 7) = (2-3a, 3-5a, 4-3a)

ð If a = -1, then L.H.S = R.H.S, thus

The point C lies on the line joining AB,

Hence, the three points are colinear.