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JEE Main202227 Jun 2022Evening ShiftMathematicsThree Dimensional GeometryActual

The shortest distance between the lines x - 3 2 = y - 2 3 = z - 1 - 1 and x + 3 2 = y - 6 1 = z - 5 3 is

Options

  1. A18 5
  2. B22 3 5
  3. C46 3 5
  4. D6 3

Correct answer

A. 18 5

Step-by-step solution

Given equation of lines x - 3 2 = y - 2 3 = z - 1 - 1 & x + 3 2 = y - 6 1 = z - 5 3 Now let the point be A = 3 , 2 , 1 on first line and B = - 3 , 6 , 5 on second line, so B A → = 6 i ^ - 4 j ^ - 4 k ^ And direction ratio's be n 1 → = 2 i ^ + 3 j ^ - k ^ & n 2 → = 2 i ^ + i ^ - 3 k ^ n 1 → × n 2 → = i ^ j ^ k ^ 2 3 - 1 2 1 3 = 10 i ^ - 8 j ^ - 4 k ^ We know that shortest Distance = B A → n 1 → n 2 → n 1 → × n 2 → B A → n 1 → n 2 &

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