BITSAT Mathematics Question (2024) — Solution

Step-by-step solution

The given equations are 3 l+m+5 n=0 ...(i) and 6 mn -2 n l+5 l m =0 ...(ii) From (i), we have m=-3 l-5 n. Putting m =-3 l-5 n in (ii), we get 6(-3 l-5 n) n-2 n l+5 l(-3 l-5 n)=0 (n+l)(2 n+l)=0 either l=- n or l=-2 n . If l=-n, then putting l=-n in (i), we obtain m=-2 n. If l=-2 n , then putting l=-2 n in (i), we obtain m = n . Thus, the direction ratios of two lines are - n ,- 2 n , n and -2 n , n , n i.e., 1,2,-1 and -2,1,1. Hence, the direction cosines are 1 6 , 2 6 , -1 6 or -2 6 , 1 6 , 1 6 . The angle between the lines is given by aligned & = 1 6 -2 6 + 2 6 1 6 + -1 6 1 6 = -1 6 \\ & = ^ -1 ( -1 6 ) aligned