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JEE Main202310 Apr 2023Morning ShiftMathematicsThree Dimensional GeometryActual

The shortest distance between the lines x + 2 1 = y - 2 = z - 5 2 and x - 4 1 = y - 1 2 = z + 3 0 is

Options

  1. A8
  2. B6
  3. C7
  4. D9

Correct answer

D. 9

Step-by-step solution

Given, x + 2 1 = y - 2 = z - 5 2 x - 4 1 = y - 1 2 = z + 3 0 Now we know that, Shortest distance between two skew lines is given by, S D = a 2 → - a 1 → n 1 → × n 2 → n 1 → × n 2 → Now finding, n 1 → × n 2 → = i ^ j ^ k ^ 1 - 2 2 1 2 0 ⇒ n 1 → × n 2 → = - 4 i ^ + 2 j ^ + 4 k ^ And a 2 → - a 1 → = 4 i ^ + j ^ - 3 k ^ - - 2 i ^ + 0 j ^ + 5 k ^ = 6 i ^ + j ^ - 8 k ^ Now putting the value in formula we get, S D = 6 i ^ + j

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