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MHT CET202016 Oct 2020Evening ShiftMathematicsThree Dimensional GeometryActual

If the plane 2 x+3 y+5 z=1 intersects the co-ordinate axes at the points A, B, C , then the centroid of ABC is

Options

  1. A( 3 2 , 1, 3 5 )
  2. B( 1 2 , 1 3 , 1 5 )
  3. C( 1 6 , 1 9 , 1 15 )
  4. D(2,3,5)

Correct answer

C. ( 1 6 , 1 9 , 1 15 )

Step-by-step solution

(D) Given equation of plane can be rewritten as x ( 1 2 ) + y ( 1 3 ) + z ( 1 5 ) =1 i.e. intercepts on X , Y , Z axis are 1 2 , 1 3 , 1 5 respectively. A = ( 1 2 , 0,0 ), B = (0, 1 3 , 0 ), C = (0,0, 1 5 ) Thus centroid of ABC = ( 1 2 +0+0 3 , 0+ 1 3 +0 3 , 0+0+ 1 5 3 )= ( 1 6 , 1 9 , 1 15 )

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