If the direction cosines l, ~m , n of two lines are connected by relations l-5 m+3 n=0 and 7 l^2+5 ~m ^2-3 n ^2=0 , then value of l+ m + n is

Step-by-step solution

aligned & l-5 ~m +3 n =0 and 7 l^2+5 ~m ^2-3 n ^2=0 & l=5 ~m -3 n and 7 l^2=3 n ^2-5 ~m ^2 aligned Putting l=(5 ~m -3 n ) in 7 l^2=3 n ^2-5 ~m ^2 , we get aligned & 7(5 m-3 n)^2=3 n^2-5 m^2 & 7 (25 m^2-30 m n+9 n^2 )=3 n^2-5 m^2 & 180 m^2-210 m n+60 n^2=0 & 6 m^2-7 m n+2 n^2=0 & (3 m-2 h)(2 m-n)=0 & 3 m=2 n or 2 m=n aligned If 3 ~m =2 n , then l= n 3 m 2 = n 3 = l 1 = 1 14 l+ m + n = 6 14 If 2 ~m = n , then l= - n 2 m 1 = n 2 = l -1 = 1 6 l+ m + n = 2 6 The possible values of l+ m + n is 2 6 or 6 14