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AP EAMCET202316 May 2023Morning ShiftMathematicsStraight LinesActual

If the plane 56 x+4 y+9 z=2016 meets the coordinate axes in A, B and C , then the centroid of the A B C is

Options

  1. A(12,168,224)
  2. B(12,168,112)
  3. C(12,168, 224 3 )
  4. D(12,168, 224 )

Correct answer

C. (12,168, 224 3 )

Step-by-step solution

The given equation of plane is : 56 x+4 y+9 z=2016 aligned & 56 x 2016 + y 504 + z 224 =1 & x 36 + y 504 + z 224 =1 aligned Then co-ordinate of A, B and C are (36,0,0),(0,504,0) and (0,0,224) . Now, the centroid is ( 36+0+0 3 , 0+504+0 3 , 0+0+224 3 ) Centroid = (12,168, 224 3 ) .

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