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JEE Main202127 Aug 2021Evening ShiftMathematicsThree Dimensional GeometryActual

The angle between the straight lines, whose direction cosines l , m , n are given by the equations 2 l + 2 m - n = 0 and m n + n l + lm = 0 , is:

Options

  1. Aπ 3
  2. Bπ 2
  3. Ccos - 1 8 9
  4. Dπ - cos - 1 4 9

Correct answer

B. π 2

Step-by-step solution

Given equations of direction cosies 2 ℓ + 2 m - n = 0   . . . . . . . . . . . . . . . i m n + n ℓ + ℓ m = 0 . . . . . . . . . . . . . . i i ℓ m + n ( ℓ + m ) = 0 From equation i n = 2 ℓ + m ℓ m + 2 ( ℓ + m ) 2 = 0 2 ℓ 2 + 2 m 2 + 5 ℓ m = 0 Dividing by m 2 on both sides 2 ℓ m 2 + 2 + 5 ℓ m = 0 Let ℓ m = t 2 t 2 + 5 t + 2 = 0 2 t 2 + 4 t + t + 2 = 0 t + 2 2 t + 1 = 0 t = - 2 , - 1 2 Case 1 ℓ m = − 1 2 m = − 2 ℓ

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