Question

Find the direction cosines l, m, n of a line which are connected by the relations l + m + n = 0, 2mn + 2ml – nl = 0.

Answer 1

Given, l + m + n = 0 ..... (1) 

2mn + 2ml – nl = 0 ..... (2) 

From (1), n = – (l + m). 

Putting n = – (l + m) in equation (2), we get, 

– 2m(l + m) + 2ml + (l + m) l = 0 

or, – 2ml – 2m² + 2ml + l² + ml = 0 

or, l² + ml – 2m² = 0