Let co-ordinates of foot of perpendicular are ( a, b, c ).

Since

Then,

Here all alternates give a =1, then k = –1. So foot is (1, 2, 3) and perpendicular distance between (1, 2, 3) and (2, – 1, 5) is .

Trick : The foot must satisfy the line, so obviously
(1,2,3) satisfies. Now length of perpendicular is distance between the foot and the point i.e. . But students should remember here that it is not necessary that the line segment joining (2, – 1, 5) and (1, 2, 3) is perpendicular to the given line, so they should check. Therefore, direction ratios of the line joining (2, – 1, 5) and (1, 2, 3) are (– 1, 3, – 2) and that of given line are (10, – 4, – 11). Hence the lines are perpendicular.