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AP EAMCET202017 Sep 2020Evening ShiftMathematicsThree Dimensional GeometryActual

If origin is the centroid of the triangle (P Q R ) with vertices (P(2 a, 2,6), Q(-4,3 b,-10) ) and (R(8,14,2 c) ), then the values of (a, b, c ) respectively are

Options

  1. A(2, 16 3 ,-2 )
  2. B(-2,- 16 3 ,-2 )
  3. C(-2,- 16 3 , 2 )
  4. D(-2, 16 3 ,-2 )

Correct answer

C. (-2,- 16 3 , 2 )

Step-by-step solution

Centroid is given by, ( aligned & x= x₁+x₂+x₃ 3 & y= y₁+y₂+y₃ 3 & z= z₁+z₂+z₃ 3 aligned ) Using values given, (0= 2 a-4+8 3 a=-2 ) Also, ( 0= 2+3 b+14 3 , b= -16 3 ) and ( 0= 6-10+2 C 3 , c=2 )

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