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AP EAMCET202318 May 2023Morning ShiftMathematicsThree Dimensional GeometryActual

If the foot of the perpendicular drawn from (0,0,0) to a plane is (1,2,3) , then equation of the plane is

Options

  1. A2 x+y+3 z=14
  2. Bx+2 y+3 z=14
  3. Cx+2 y+3 z+14=0
  4. Dx+2 y-3 z=14

Correct answer

B. x+2 y+3 z=14

Step-by-step solution

Foot of perpendicular lies on the plane. So, the equation of plane is a(x-1)+b(y-2)+c(z-3)=0 ...(i) Line joining (0,0,0) and (1,2,3) is perpendicular to the plane (i). a=1-0=1, b=2-0=2, c=3-0=3 So, equation (i) reduces to aligned & 1(x-1)+2(y-2)+3(z-3)=0 & x+2 y+3 z=14 aligned

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