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If the direction cosines of two lines are given by l+3 m+5 n=0 and 5 l m-2 m n+6 l n=0 . then the angle between the lines is

Options

  1. A⁻¹ ( 1 6 )
  2. B⁻¹ ( 1 3 )
  3. C⁻¹ ( 1 5 )
  4. D⁻¹ ( 1 6 )

Correct answer

A. ⁻¹ ( 1 6 )

Step-by-step solution

We have, and l+3 m+5 n=0 and 5 m-2 m n+6 l n=0 On substituting the value of l from Eq. (i) in Eq. (ii), we get array rcr & 5(-3 m-5 n) m-2 m n+6(-3 m-5 n) n=0 & -15 m^2-25 m n-2 m n-18 m n-30 n^2=0 & 15 m^2+45 m n+30 n^2=0 & m^2+3 m n+2 n^2=0 & (m+n)(m+2 n)=0 & m=-n or m=-2 n array When m=-n_ r then l=-2 n and thus the DR'S are 2. -1,1 . When m=-2 n , then l=n and thus the DR'S are 1,1,-2 . Hence, the DR's of given lines are 2,-1,1 and 1,1,-2 . Now, let be the acute angle between the given Ines, then aligned & = 2

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