If the d.c’s (l,m,n) of two lines are connected by the relations l+m+n=0, 2lm−mn+2nl=0 then the d.c’s of the two lines are

l+m+n=0⇒l=−m−n2lm−mn+2nl=0⇒(−m−n)−nm+2n(−m−n)=0⇒−2m2−2nm−mn−2mn−2n2=0⇒2m2+5mn+2n2=0⇒(2m+n)(m+2n)=0⇒2m+n=0 or m+2n=0 If 2m+n=0 then m=k,n=−2k,l=kD.r’s of one line are (k,−k,−2k)=(1,1,−2)If m+2n=p then n=p,m=−2p,l=pD.r’s of second line are (p,−2p,p)=(1,−2,1)