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JEE Main20198 Apr 2019Morning ShiftMathematicsThree Dimensional GeometryActual

The length of the perpendicular from the point ( 2 , - 1 , 4 ) on the straight line x + 3 10 = y - 2 - 7 = z 1 is

Options

  1. Agreater than 3 but less than 4
  2. Bgreater than 4
  3. Cless than 2
  4. Dgreater than 2 but less than 3

Correct answer

A. greater than 3 but less than 4

Step-by-step solution

Let P 2 , - 1,4 Now, any point Q on line x + 3   10 = y - 2 - 7 = z 1 = λ is Q = 10 λ - 3 ,   - 7 λ + 2   , λ Direction Ratio of P Q = 10 λ - 3 - 2 ,   - 7 λ + 2 + 1 ,     λ - 4 = 10 λ - 5 ,   - 7 λ + 3 ,   λ - 4 ∵ P Q   is perpendicular to given line ∴ 10 10 λ - 5 - 7 - 7 λ + 3 +   λ - 4 = 0 ⇒ 150   λ = 75   ⇒ λ = 1 2 ∴ Q ≡ 2 , - 3 2 , 1 2 Distan

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