If (l₁, m₁, n₁ ) and (l₂, m₂, n₂ ) are the direction cosines of two lines satisfying the relations l^2+m n-6 n^2=0 and 2 l-m+3 n=0 , then |l₁ l₂ |+ |m₁ m₂ |=

Step-by-step solution

2 l-m+3 n=0 [Given] m=2 l+3 n Substitute this value of m in l^2+m n-6 n^2=0 aligned & l^2+(2 l+3 n) n-6 n^2=0 & l^2+2 l n-3 n^2=0 & l= -2 n 4 n^2+12 n^2 2 & l= -2 n+4 n 2 , -2 n-4 n 2 & l=n,-3 n aligned Substitute these value in m=2 l+3 n m=5 n,-3 n DR's are (n, 5 n, n) and (-3 n,-3 n, n) . DC's are ( 1 3 3 , 5 3 3 , 1 3 3 ) and ( -3 19 , -3 19 , 1 19 ) Here l₁= 1 3 3 , l₂= -3 19 , m₁= 5 3 3 , m₂= -3 19 aligned & |l₁ l₂ |+ |m₁ m₂ | &= | -1 3 19 |+ | -5 3 19 | & = 6 3 19 = 2 3 19 aligned