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

Step-by-step solution

Given, l+m+n=0, l=-m-n and l^2+m^2-n^2=0 aligned & (-m-n)^2+m^2-n^2=0 & 2 m^2+2 m n=0 & 2 m(m+n)=0 & m=0 or m+n=0 & aligned If m=0 , then l=-n l₁ -1 = m₁ 0 = n 1 and if m+n=0 m=-n , then l=0 array ll & l₂ 0 = m₂ -1 = n₂ 1 ie, & (l₁, m₁, n₁ )=(-1,0,1) and & (l₂, m₂, n₂ )=(0,-1,1) & = 0+0+1 1+0+1 0+1+1 = 1 2 & = 3 array