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JEE Main202325 Jan 2023Evening ShiftMathematicsThree Dimensional GeometryActual

The shortest distance between the lines x + 1 = 2 y = - 12 z and x = y + 2 = 6 z - 6 is

Options

  1. A2
  2. B3
  3. C5 2
  4. D3 2

Correct answer

A. 2

Step-by-step solution

Given, Equation of the lines x + 1 = 2   y = - 12 z and x = y + 2 = 6 z - 6 ⇒ x + 1 1 = y 1 2 = z - 1 12 and x 1 = y + 2 1 = z - 1 1 6 We know that, shortest distance between the lines is given by S . D = b → - a → · p → × q → p → × q → Here p → = i ^ + j ^ 2 + - k ^ 12   &   q → = i ^ + j ^ + k ^ 6 and a → = i ^   &   b → = 2 j ^ - k ^ ⇒ S . D = - i ^ + 2 j ^ - k ^ · p → × q &#859

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