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MHT CET202519 Apr 2025Morning ShiftMathematicsThree Dimensional GeometryActual

The distance of the point (-3,2,3) from the line passing through (4,6,-2) and having direction ratios -1,2,3 is ________ units.

Options

  1. A2 17
  2. B4 17
  3. C2 19
  4. D4 19

Correct answer

C. 2 19

Step-by-step solution

The distance from point P(-3,2,3) to the line through A(4,6,-2) with direction vector b = - i + 2 j + 3 k is determined by the formula d = | AP b | | b | . The vector AP = P - A = -7 i - 4 j + 5 k . The cross product yields AP b = -22 i + 16 j - 18 k , with magnitude | AP b | = 484 + 256 + 324 = 1064 . The magnitude of the direction vector is | b | = 1 + 4 + 9 = 14 . Thus, the distance becomes d = 1064 14 = 1064 14 = 76 = 2 19 . This corresponds to option C.

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