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JEE Main202427 Jan 2024Morning ShiftMathematicsThree Dimensional GeometryActual

The distance, of the point ( 7 , - 2 , 11 ) from the line x - 6 1 = y - 4 0 = z - 8 3 along the line x - 5 2 = y - 1 - 3 = z - 5 6 , is :

Options

  1. A12
  2. B14
  3. C18
  4. D21

Correct answer

B. 14

Step-by-step solution

Given lines are x - 6 1 = y - 4 0 = z - 8 3 and x - 5 2 = y - 1 - 3 = z - 5 6 . Let, A B be a line parallel to x - 5 2 = y - 1 - 3 = z - 5 6 which intersects x - 6 1 = y - 4 0 = z - 8 3 at point B , where A ≡ 7 , - 2 , 11 So, equation of A B is, x - 7 2 = y + 2 - 3 = z - 11 6 = λ let ⇒ x = 2 λ + 7 , y = - 3 λ - 2 , z = 6 λ + 11 ⇒ B ≡ ( 2 λ + 7 , - 3 λ - 2 , 6 λ + 11 ) Also, the point B lies on x - 6 1 = y - 4 0 = z - 8 3 . ⇒ 2 λ + 7 - 6 1 = - 3 λ - 2 - 4 0 = 6 λ + 11 - 8 3 ⇒ - 3 λ - 2 - 4 = 0 ⇒ - 3 λ = 6 ⇒ λ = - 2

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