Show that the points $(2,3,4),( - 1, - 2,1),(5,8,7)$ are collinear.

.: Let $A \equiv (2,3,4),B \equiv ( - 1, - 2,1)$ and $C \equiv (5,8,7)$

Direction ratios of AB are $< ( - 1 - 2),( - 2, - 3),(1, - 4) >$ or $< - 3, - 5, - 3 >$

Direction ratios of AC are $< (5 - 2),(8 - 3),(7 - 4) >$ or $< 3,5,3 >$

It is clear that the direction ratios of AB and AC are proportional.

Hence, AB and AC are parallel, but these have a point A in common,

therefore , AB and AC are along the same line.

Hence A, B and C are collinear.