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MHT CET202522 Apr 2025Morning ShiftMathematicsThree Dimensional GeometryActual

If the sum of the squares of the distances of a point P(x, y, z) from the three co-ordinate axes is 324 , then the distance of point P from the origin is ....

Options

  1. A18
  2. B162
  3. C9 2
  4. D324

Correct answer

C. 9 2

Step-by-step solution

Distance from the origin: A point P(x, y, z) has an origin distance of x^2 + y^2 + z^2 . Sum of squared axis distances: The squared distances from the axes are y^2 + z^2 , x^2 + z^2 , and x^2 + y^2 . Their sum is given as 324. Combine terms: 2x^2 + 2y^2 + 2z^2 = 324 , so x^2 + y^2 + z^2 = 162 . Thus, the distance is 162 = 81 2 = 9 2 . The correct option is C .

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