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JEE Main202628 January 2026Evening ShiftMathematicsThree Dimensional GeometryActual

Let Q ( a , b , c ) be the image of the point P (3,2,1) in the line x-1 1 = y 2 = z-1 1 . Then the distance of Q from the line x-9 3 = y-9 2 = z-5 -2 is

Options

  1. A8
  2. B5
  3. C7
  4. D6

Correct answer

C. 7

Step-by-step solution

Line 1 passes through (1, 0, 1) with direction (1, 2, 1) . Point on line: (1+t, 2t, 1+t) . For projection Q of P(3, 2, 1): (t-2, 2t-2, t) (1, 2, 1) = 0 gives 6t = 6 , so t = 1 . Thus Q = (2, 2, 2). Distance from Q to line 2 (passing through (9, 9, 5) with direction (3, 2, -2) ): QR = (7, 7, 3) . QR d = -20 i + 23 j - 7 k . | QR d | = 400 + 529 + 49 = 978 . | d | = 17 . Distance = 978 17 = 57.53 7.59 7 .

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