Given l+3m+5n=0 .......(1) and 5lm−2mn+6nl=0 .......(2) From eq. (1) we have l=−3m−5n Put the value of l in eq. (2), we get; Put the value of l in eq. (2), we get; 5(−3m−5n)m−2mn+6n(−3m−5n)=0 ⇒15m2+45mn+30n2=0 ⇒m2+3mn+2n2=0 ⇒m2+2mn+mn+2n2=0 ⇒(m+n)(m+2n)=0 ∴m=−n or m=−2n For m=−n,l=−2n And for m=−2n,l=n ∴(l,m,n)=(−2n,−n,n) Or (l,m,n)=(n,−2n,n) ⇒(l,m,n)=(−2,−1,1) Or (l,m,n)=(1,−2,1) Therefore, angle between the lines is given as: