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JEE Main20231 Feb 2023Morning ShiftMathematicsThree Dimensional GeometryActual

The shortest distance between the lines x - 5 1 = y - 2 2 = z - 4 - 3 and x + 3 1 = y + 5 4 = z - 1 - 5 is

Options

  1. A7 3
  2. B5 3
  3. C6 3
  4. D4 3

Correct answer

C. 6 3

Step-by-step solution

Shortest distance between two lines x - x 1 a 1 = y - y 1 b 1 = z - z 1 c 1 and x - x 2 a 2 = y - y 2 b 2 = z - z 2 c 2 is given as x 1 - x 2 y 1 - y 2 z 1 - z 2 a 1 b 1 c 1 a 2 b 2 c 2 a 1 b 2 - a 2 b 1 2 + b 1 c 2 - b 2 c 1 2 + c 1 a 2 - c 2 a 1 2 = 5 - - 3   2 - - 5   4 - 1 1 2 - 3 1 4 - 5 4 - 2 2 + - 10 + 12 2 + - 3 + 5 2 = 8 7 3 1 2 - 3 1 4 - 5 2 2 + 2 2 + 2 2 = 8 - 10 + 12 - 7 - 5 + 3 + 3 4 - 2 4 + 4 + 4 = 16 + 14 + 6 12 = 36 2 3 = 18 3 = 6 3

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