ExamBro
ExamBro
TS EAMCET · Maths · Three Dimensional Geometry

If the direction ratio of two lines are given by \(3 l m-4 l n+m n=0\) and \(l+2 m+3 n=0\), then the angle between the lines, is :

  1. A \(\frac{\pi}{6}\)
  2. B \(\frac{\pi}{4}\)
  3. C \(\frac{\pi}{6}\)
  4. D \(\frac{\pi}{2}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{\pi}{2}\)

Step-by-step Solution

Detailed explanation

We have, \(3 l m-4 l n+m n=0\) \(\ldots\) (i) and \(l+2 m+3 n=0\) \(\ldots\) (ii) From Eq. (ii), \(l=-(2 m+3 n)\) Using in Eq. (i), we get \(-3(2 m+3 n) m+4(2 m+3 n) n+m n=0\) \(\Rightarrow \quad-6 m^2-9 m n+8 m n+12 n^2+m n=0\) \(\Rightarrow \quad-6 m^2+12 n^2=0\) Now,…