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JEE Main202621 January 2026Evening ShiftMathematicsThree Dimensional GeometryActual

Let the line L ₁ be parallel to the vector -3 i +2 j +4 k and pass through the point (2,6,7), and the line L ₂ be parallel to the vector 2 i + j +3 k and pass through the point (4,3,5) . If the line L ₃ is parallel to the vector -3 i +5 j +16 k and intersects the lines L ₁ and L ₂ at the points C and D, respectively, then | C D |² is equal to :

Options

  1. A89
  2. B312
  3. C171
  4. D290

Correct answer

D. 290

Step-by-step solution

L₁ : x-2 -3 = y-6 2 = z-7 4 Point C on L₁ : (-3 ₁ + 2, 2 ₁ + 6, 4 ₁ + 7) L₂ : x-4 2 = y-3 1 = z-5 3 Point D on L₂ : (2 ₂ + 4, ₂ + 3, 3 ₂ + 5) Dr's of line L₃ : L₃ : 2 ₂ + 3 ₁ + 2 -3 = ₂ - 2 ₁ - 3 5 = 3 ₂ - 4 ₁ - 2 16 ₁ = -3, ₂ = 2 C(11, 0, -5) D(8, 5, 11) | CD |^2 = 3^2 + 5^2 + 16^2 = 290

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