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MHT CET202122 Sep 2021Morning ShiftMathematicsThree Dimensional GeometryActual

If a plane meets the axes X , Y , Z in A , B , C respectively such that centroid of ABC is (1,2,3) , then the equation of the plane is

Options

  1. Ax+2 y+3 z=1
  2. Bx+ y 2 + z 3 =3
  3. Cx 3 + y 6 + z 9 =1
  4. Dx 4 + y 8 + z 12 =1

Correct answer

C. x 3 + y 6 + z 9 =1

Step-by-step solution

Let A=(x, 0,0) ; B=(0, y, 0) ; C=(0,0, z) Centroid of A B C is (1,2,3) x 3 =1, y 3 =2, z 3 =3 ( x , y , z )=(3,6,9) Hence equation of required plane is x 3 + y 6 + z 9 =1

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