∵l,m and n are the direction cosines of any line. ∴l2+m2+n2=1...(i) Given, l−m+n=0 ⇒l=m−n and lm+mn−4nl=0 ⇒(m−n)m+mn−4n(m−n)=0 ⇒m2−mn+mn−4mn+4n2=0 ⇒m2+4n2−4mn=0 ⇒(m−2n)2=0 ⇒m=2n ⇒l=2n−n=n From Eq. (i), n2+4n2+n2=1 ⇒n=±