The acute angle between the two lines whose direction ratios are given by l+m-n=0 and l^2+m^2-n^2=0 , is

Step-by-step solution

Given that l+m-n=0 and l^2+m^2-n^2=0 From equaion (i) l=-(m-n) Putting in equation (ii), we get aligned & (m-n)^2+m^2-n^2 & =0 & m^2+n^2-2 m n+m^2-n^2 & =0 & 2 m^2-2 m n & =0 & 2 m(m-n) & =0 & m=0, m & =n aligned From equation (i), if m=0 , then l=n l: m: n=1: 0: 1 If m=n , then l=0 l: m: n=0: 1: 1 If is the acute angle, then aligned & = | 1.0+0.1+1.1 1+1 1+1 |= 1 2 = 3 & = 3 aligned