Find the direction cosines of a line which is perpendicular to the lines whose direction ratios are

1) – 1 / √35, 5 / √35, 3 / √35

2) 13 / √35, – 1 / √35, 1 / √35

3) 2 / √3, 5 / √3, 7 / √3

4) 3 / √35, 5 / √35, 7 / √35

Solution: (1) – 1 / √35, 5 / √35, 3 / √35

Let direction ratios of line be a, b, c

a – b + 2c = 0 — (i)

2a + b – c = 0 — (ii)

Solving (i) and (ii), we get

a = – 1, b = 5, c = 3

The direction ratios of line = (- 1, 5, 3)

The required direction cosines = – 1 / √35, 5 / √35, 3 / √35