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MHT CET202013 Oct 2020Morning ShiftMathematicsThree Dimensional GeometryActual

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

Options

  1. A6 units
  2. B13 units
  3. C10 units
  4. D7 units

Correct answer

A. 6 units

Step-by-step solution

Given x-3 1 = y-4 2 = z-5 2 = (say) ...(1) Hence coordinates of any point on this line are x= +3, y=2 +4, z=2 +5 Since this point lies on the plane, we write array l ( +3)+(2 +4)+(2 +5)=2 5 +12=2 =-2 array Hence coordinates of point of inter section are (-2+3,-4+4,-4+5) i.e. (1,0,1) Distance between (3,4,5) and (1,0,1) is = (3-1)²+(4-0)²+(5-1)² =6

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