If the direction cosines of two lines are connected by the relations l+3m+5n=0  and  2l2−5m2+n2=0, then the sum of all possible values of mn  is

The given relations are l+3m+5n=0  and  2l2−5m2+n2=0From the first relation l=3m+5n, substitute this in the second equation     23m+5n2−5m2+n2=018m2+50n2−5m2+n2+30mn=013m2+51n2+30mn=0      Divide both sides by  n2It gives   13mn2+30mn+51=0          Sum of all the values  of mn  is  −3013