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MHT CET202313 May 2023Morning ShiftMathematicsThree Dimensional GeometryActual

The distance of the point (-1,-5,-10) from the point of intersection of the line x-2 3 = y+1 4 = z-2 12 and the plane x-y+z=5 is

Options

  1. A13 units.
  2. B12 units.
  3. C5 units.
  4. D16 units.

Correct answer

A. 13 units.

Step-by-step solution

Let x-2 3 = y+1 4 = z-2 12 = The co-ordinates of any point on the line are P (3 +2,4 -1,12 +2) This point lies on the plane aligned & x-y+z=5 & 3 +2-(4 -1)+12 +2=5 & 11 =0 & =0 & P (2,-1,2) & Let Q (-1,-5,-10) & PQ = (-1-2)^2+(-5+1)^2+(-10-2)^2 & = 9+16+144 & =13 units & aligned

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