The angle between the lines whose direction cosines are given by the equations l^2+m^2-n^2=0 and l+m+n=0 is

Step-by-step solution

Given, aligned l^2+m^2-n^2 & =0 ...(i) l+m+n & =0 ...(ii) aligned By Eq. (ii), n=-(l+m) Put it Eq. (i), l^2+m^2=n^2 array lc & l^2+m^2=[-(l+m)]^2 & l^2+m^2=l^2+m^2+2 l m & 2 l m=0 & l=0 or m=0 & n=-m or n=-l & l^2+m^2+n^2=l and l^2+m^2+n^2=1 & 0+m^2+m^2=l and l^2+l^2=1 array gathered 2 m^2=1 and l^2= 1 2 m= 1 2 and l= 1 2 gathered Direction cosine (0, 1 2 ,- 1 2 ) and (0,- 1 2 , 1 2 ) or ( 1 2 , 0,- 1 2 ) and (- 1 2 , 0, 1 2 ) Direction of two lines array r (l₁, m₁, n₁ )= (0, 1 2 ,- 1 2 ) (l₂, m₂, n₂ )= ( 1 2 , 0,-