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COMEDK2023Evening ShiftMathematicsThree Dimensional GeometryActual

If the direction ratios 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

Options

  1. A4
  2. B3
  3. C6
  4. D2

Correct answer

D. 2

Step-by-step solution

Given the equations for direction ratios (l, m, n) are 3lm - 4ln + mn = 0 and l + 2m + 3n = 0 . From the second equation, l = -2m - 3n . Substituting this into the first equation: 3(-2m - 3n)m - 4(-2m - 3n)n + mn = 0 -6m^2 - 9mn + 8mn + 12n^2 + mn = 0 -6m^2 + 12n^2 = 0 m^2 = 2n^2 , which implies m = 2 n . Case 1: m = 2 n . Then l = -2( 2 n) - 3n = -(2 2 + 3)n . The direction ratios are (-(2 2 + 3), 2 , 1) . Let this be vector v₁ . Case 2: m = - 2 n . Then l = -2(- 2 n) - 3n = (2 2 - 3)n . The direction ratios are (

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