If a direction cosines l, m, n of a line are connected by relation l+2 m+n=0,2 l-2 m+3 n=0 , then what is the value of l^2+m^2-n^2 ?

Step-by-step solution

l+2 m+n=0 ....(i) and 2 l-2 m+3 n=0 ....(ii) From (i) we have l=-2 m-n ....(iii) Putting the value of l in (ii) aligned & 2(-2 m-n)-2 m+3 n=0 & -4 m-2 n-2 m+3 n=0 & n=6 m & Now, & l=-2 m-n & =-2 m-6 m=-8 m & l -8 m = m n = n 6 m & l -8 = m 1 = n 6 & = l^2+m^2+n^2 (-8)^2+(1)^2+(6)^2 = 1 101 & l= -8 101 , m= 1 101 & n= 6 101 aligned Direction consines of a line aligned & ( -8 101 , 1 101 , 6 101 ) & aligned l^2+m^2-n^2 & = 64 101 + 1 101 - 36 101 & = 29 101 aligned aligned