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JEE Main202623 January 2026Morning ShiftMathematicsThree Dimensional GeometryActual

The vertices B and C of a triangle ABC lie on the line x 1 = 1-y -2 = z -2 3 . The coordinates of A and B are (1,6,3) and (4,9, ) respectively and C is at a distance of 10 units from B. The area (in sq. units) of ABC is :

Options

  1. A20 13
  2. B5 13
  3. C15 13
  4. D10 13

Correct answer

B. 5 13

Step-by-step solution

4 1 = 9-1 2 = - 2 3 = 14 AD ( i + 2 j + 3 k ) = 0 ( - 1) i + (2 - 5) j + (3 - 1) k = AD - 1 + 4 - 10 + 9 - 3 = 0 14 = 14 = 1 D = (1, 3, 5) AD = 3^2 + 2^2 = 13 Ar( ABC) = 1 2 13 10 = 5 13

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