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JEE Main202325 Jan 2023Morning ShiftMathematicsThree Dimensional GeometryActual

Consider the lines L 1 and L 2 given by L 1 : x - 1 2 = y - 3 1 = z - 2 2 L 2 : x - 2 1 = y - 2 2 = z - 3 3 A line L 3 having direction ratios 1 , - 1 , - 2 , intersects L 1 and L 2 at the points P and Q respectively. Then the length of line segment P Q is

Options

  1. A2 6
  2. B3 2
  3. C4 3
  4. D4

Correct answer

A. 2 6

Step-by-step solution

Given, The lines L 1 and L 2 given by L 1 : x - 1 2 = y - 3 1 = z - 2 2 L 2 : x - 2 1 = y - 2 2 = z - 3 3 Now any point on line L 1 is given by, P = 2 λ + 1 , λ + 3 , 2 λ + 2 And any point on line L 2 is given by, Q = μ + 2 , 2 μ + 2 , 3 μ + 3 Now equation of line L 3 which passes through Q is given by,   x - μ + 1 1 = y - 2 μ + 2 - 1 = z - 3 μ + 3 - 2 Now it also passes through P , so we get, ⇒     2 λ - μ - 1 1 = λ - 2 μ + 1 - 1

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