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JEE Main20266 April 2026Evening ShiftMathematicsThree Dimensional GeometryActual

The shortest distance between the lines x-4 1 = y-3 2 = z-2 -3 and x+2 2 = y-6 4 = z-5 -5 is :

Options

  1. A5 6 6
  2. B2 5
  3. C3 5
  4. D4 5

Correct answer

C. 3 5

Step-by-step solution

The given lines are L₁: x-4 1 = y-3 2 = z-2 -3 and L₂: x+2 2 = y-6 4 = z-5 -5 . For L₁ , a point on the line is a ₁ = 4 i + 3 j + 2 k and its direction vector is b ₁ = i + 2 j - 3 k . For L₂ , a point on the line is a ₂ = -2 i + 6 j + 5 k and its direction vector is b ₂ = 2 i + 4 j - 5 k . The shortest distance d between two skew lines is given by d = |( a ₂ - a ₁) ( b ₁ b ₂)| | b ₁ b ₂| . We have a ₂ - a ₁ = (-2 - 4) i + (6 - 3) j + (5 - 2) k = -6 i + 3 j + 3 k . The cross product of the direction vectors is: b ₁

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