The angle between the lines whose direction cosines satisfy the equations
l+m+n=0 and l2=m2+n2, is
π3
We know that, angle between two lines is
cos θ=a1a2+b1b2+c1c2√a21+b21+c21√a22+b22+c22l+m+n=0⇒l=−(m+n)⇒(m+n)2=l2⇒m2+n2+2mn=m2+n2 [∵2=m2+n2,given]⇒2mn=0When m=0⇒ l=−nHence, (l,m,n) is (1,0,−1).When n=0, then l=−mHence,(l,m,n) is (1,0,−1).∴ cos θ=1+0+0√2×√2=12⇒θ=π3