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JEE Main20238 Apr 2023Morning ShiftMathematicsThree Dimensional GeometryActual

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

Options

  1. A6 3
  2. B2 6
  3. C6 2
  4. D3 6

Correct answer

D. 3 6

Step-by-step solution

Given: x - 4 4 = y + 2 5 = z + 3 3 x - 1 3 = y - 3 4 = z - 4 2 So, a → 1 = 4 i ^ - 2 j ^ - 3 k ^ a → 2 = i ^ + 3 j ^ + 4 k ^ So, a → 2 - a → 1 = - 3 i ^ + 5 j ^ + 7 k ^ And, b → 1 × b → 2 = i ^ j ^ k ^ 4 5 3 3 4 2 = - 2 i ^ + j ^ + k ^ ⇒ b → 1 × b → 2 = - 2 2 + 1 2 + 1 2 = 6 Shortest distance between the lines = a → 2 - a → 1 · b → 1 × b → 2 b → 1 × b → 2 = - 3 i ^ + 5 j ^ + 7 k ^ · - 2 i ^ + j ^

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