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AP EAMCET201822 Apr 2018Morning ShiftMathematicsThree Dimensional GeometryActual

A plane cuts the coordinate axes X, Y, Z at A , B, C respectively such that the centroid of the A B C is (6,6,3) . Then the equation of that plane is

Options

  1. Ax+y+z-6=0
  2. Bx+2 y+z-18=0
  3. C2 x+y+z-18=0
  4. Dx+y+2 z-18=0

Correct answer

D. x+y+2 z-18=0

Step-by-step solution

Let the equation of the plane is x a + y b + z c =1 By the definition of the centroi ( a 3 , b 3 , c 3 )=(6,6,3) Therefore, aligned a & =18 b & =18 c & =9 aligned The equation of the plane becomes array rlrl & & x 18 + y 18 + z 9 & =1 x+y+2 z 18 =1 & x+y+2 z & =18 x+y+2 z-18 & =0 array

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