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Let the direction cosines of two lines satisfy the equations 31+2 m+n=0 and 2 m n-3 n l+5 l m=0 . If is the angle between these two lines, then =

Options

  1. A19 28
  2. B3 28
  3. C25 2991
  4. D1 6

Correct answer

C. 25 2991

Step-by-step solution

3 l+2 m+n=0 ...(1) and 2 m n-3 n l+5 m l=0 ...(2) aligned & n(2 m-3 l)+5 m l=0 n=-(2 m+3 l) & -(2 m+3 l)(2 m-3 l)+5 m l=0 & 9 l^2-4 m^2+5 m l=0 & 9 l^2+5 m l-4 m^2=0 & 9 ( l m )^2+5 ( l m )-4=0 aligned If l m =t then 9 t^2+5 t-4=0 aligned & 9 t(t+1)-4(t+1)=0 t=-1, 4 9 & l m =-1 l=-m & n=-(2 m+3 l)=-(2 m-3 m)=m aligned t: m: n=-m: m: m=-1: 1: 1 Also for l m = 4 9 l= 4 m 9 aligned & n=-(2 m+3 l)=- (2 m+ 4 m 3 a )= -10 m 3 & l: m: n= 4 m 9 : m: -10 m 3 & l: m: n=4: 9:-30 & Angle between lines = | -4+9-30 1^2+1^2+1^2 4

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