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MHT CET202415 May 2024Morning ShiftMathematicsProperties of TrianglesActual

The centroid of tetrahedron with vertices P (5,-7,0), Q ( a , 5,3), R (4,-6, ~b ) and S (6, c , 2) is (4,-3,2) , then the value of 2 a+3 b+c is equal to

Options

  1. A15
  2. B-7
  3. C7
  4. D-5

Correct answer

C. 7

Step-by-step solution

Centroid of tetrahedron aligned & ( 5+a+4+6 4 , -7+5-6+c 4 , 0+3+b+2 4 ) & (4,-3,2) ( 15+a 4 , -8+c 4 , b+5 4 ) aligned aligned & 15+a 4 =4 a=1 & -8+c 4 =-3 c=-4 & b+5 4 =2 b=3 & 2 a+3 b+c=2(1)+3(3)-4=7 aligned

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