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JEE Main202621 January 2026Evening ShiftMathematicsThree Dimensional GeometryActual

Let the line L pass through the point (-3,5,2) and make equal angles with the positive coordinate axes. If the distance of L from the point (-2, r , 1) is 14 3 , then the sum of all possible values of r is :

Options

  1. A10
  2. B6
  3. C12
  4. D16

Correct answer

A. 10

Step-by-step solution

Line L through (-3, 5, 2) making equal angles with axes has direction (1, 1, 1) . Point Q = (-2, r, 1) , PQ = (1, r-5, -1) . PQ d = (r-4, -2, 6-r) . | PQ d |^2 = (r-4)^2 + 4 + (6-r)^2 = 2r^2 - 20r + 56 . Distance = 2r^2 - 20r + 56 3 = 14 3 . 2r^2 - 20r + 56 = 14 r^2 - 10r + 21 = 0 r = 3 or r = 7 . Sum = 3 + 7 = 10 .

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