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AP EAMCET202315 May 2023Evening ShiftMathematicsThree Dimensional GeometryActual

Let ABCD be a tetrahedron in which the coordinates of each of its vertices are in arithmetic progression with same common difference. If the centroid G of the tetrahedron is (2,3, k ) , then the distance of G from the origin is

Options

  1. A38
  2. B7
  3. C22
  4. D29

Correct answer

D. 29

Step-by-step solution

Let coordinates of vertices of tetrahedron are aligned & A (a₁-d, a₁, a₁+d ) ; B (a₂-d, a₂, a₂+d ) ; & C (a₃-d, a₃, a₃+d ) and D (a₄-d, a₄, a₄+d ) aligned Centroid =(2,3, k) aligned & a₁+a₂+a₃+a₄-4 d=4...(i) & a₁+a₂+a₃+a₄=6 ...(ii) & a₁+a₂+a₃+a₄+4 d=2 k...(iii) aligned From (i), (ii) and (iii) we get d= 1 2 and k=4 Now distance of G from origin = 4+9+16 = 29 .

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