The angle between the lines, whose direction cosines l, ~m , n satisfy the equations l+ m + n =0 and 2 l^2+2 ~m ^2- n ^2=0 , is

Step-by-step solution

Substituting n =-l- m in aligned & 2 l^2+2 ~m ^2- n ^2=0, we get & 2 l^2+2 ~m ^2-(-l- m )^2=0 & l^2+ m ^2-2 l ~m =0 & (l- m )^2=0 & l= m aligned If l= m , then n =-2 ~m l 1 = m 1 = n -2 The direction ratios of both the lines are same. array ll & = 1 & =0^ or 180^ array