The direction ratios of a line can be found by subtracting the corresponding coordinates of two points through which the line passes i.e. (subtract x coordinates, subtract y coordinates, subtract z coordinates), this is the direction ratio of the line. There can be no direction ratio of a line passing through only one point, there should be at least two points.

For the two lines to be parallel or anti parallel to each other the fraction of their corresponding direction ratios should be equal.

The direction ratios of a line passing through the points (4,7,8) and (2,3,4) are (4–2,7–3,8–4) = (2,4,4)

The direction ratios of a line passing through the points (–1,–2,1) and (1,2,5) are (–1–1,–2–2,1–5) = (–2,–4,–4)

The direction ratios are proportional.

Hence the lines are mutually parallel and even overlapping each other because of the constant –1 or 1.