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JEE Main202329 Jan 2023Evening ShiftMathematicsThree Dimensional GeometryActual

Shortest distance between the lines x - 1 2 = y + 8 - 7 = z - 4 5 and x - 1 2 = y - 2 1 = z - 6 - 3 is

Options

  1. A2 3
  2. B4 3
  3. C3 3
  4. D5 3

Correct answer

B. 4 3

Step-by-step solution

Given lines are x - 1 2 = y + 8 - 7 = z - 4 5 and x - 1 2 = y - 2 1 = z - 6 - 3 Corresponding vectors are: a → = i ^ - 8 j ^ + 4 k ^ , p → = 2 i ^ - 7 j ^ + 5 k ^ b → = i ^ + 2 j ^ + 6 k ^ , q → = 2 i ^ + j ^ - 3 k ^ S . D . = | a → - b →       p →         q →   | | p → × q → | a → - b → = - 10 j ^ - 2 k ^ [ a → - b →       p →         q → ]

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