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MHT CET202015 Oct 2020Evening ShiftMathematicsThree Dimensional GeometryActual

The distance of the point (7,5,2) from the plane 3 x+4 y+z-8=0 measured parallel to the line x-1 3 = y-2 6 = z+1 2

Options

  1. A74 units
  2. B47 units
  3. C6 units
  4. D7 units

Correct answer

D. 7 units

Step-by-step solution

Let P=(7,5,2) Eq. of line passing through P and parallel to given line is x-7 3 = y-5 6 = z-2 2 =r (say) Hence coordinates of any point on this line are (3 r+7,6 r+5,2 r+2) Q( say ) We have 3 x+4 y+z-8=0 3(3 r+7)+4(6 r+5)+(2 r+2)-8=0 9 r+24 r+2 r+21+20+2-8=0 35 r=-35 r=-1 Q (-3+7,-6+5,-2+2) i.e. (4,-1,0) Distance between PQ (7-4)²+(5+1)²+(2-0)² = 9+36+4 =7

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