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JEE Main202225 Jul 2022Evening ShiftMathematicsThree Dimensional GeometryActual

The shortest distance between the lines x + 7 - 6 = y - 6 7 = z and 7 - x 2 = y - 2 = z - 6 is

Options

  1. A2 29
  2. B1
  3. C37 29
  4. D29 2

Correct answer

A. 2 29

Step-by-step solution

Given line L 1 : x + 7 - 6 = y - 6 7 = z - 0 1 Let any point on it is given by a → 1 - 7 , 6 , 0 and L 1 is parallel to b → 1 - 6 , 7 , 1 Also given line L 2 : x - 7 - 2 = y - 2 1 = z - 6 1 Let any point on it be a → 2 7 , 2 , 6 and L 2 is parallel to b → 2 - 2 , 1 , 1 Now finding b → 1 × b → 2 = i ^ j ^ k ^ - 6 7 1 - 2 1 1 = 3 i ^ + 2 j ^ + 4 k ^ Now shortest distance between L 1 and L 2 will be = a → 2 - a → 1 · b → 1 × b → 2 b → 1 &

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