The points (2, 3 , 4), (-1, -2, 1), (5, 8, 7)  are -

Collinear 

the given points are A(2, 3 , 4), B(-1, -2, 1) and  C(5, 8, 7)

We know that the direction ratios of the line joining the points (x₁,y₁,z₁) and (x₂,y₂,z₂) are given by (x₂-x₁), (y₂-y₁) and (z₂-z₁) 

The direction ratio of AB are (-1-2), (-2-3) and (1-4) i.e. -3, -5 and -3

The direction ratio of BC are (5 - (-1)), (8-(-2) and (7-1) i.e. 6,10 and 6

It can be seen that the direction ratios of BC are -2times that of AB i.e. they are proportional.

Therefore AB is parallel to BC. Since point B is common to both AB and BC, So points A, B and C are collinear.