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TS EAMCET · Maths · Straight Lines

\[ A(2,3,-4), B(-3,3,-2), C(-1,4,2), D(3,5,1) \] are the vertices of a tetrahedron. If \(G_1, G_2\) and \(G_3\) are the centroids of the three faces having the vertex \(D\) in common, then the centroid of the \(\Delta G_1 G_2 G_3\) is

  1. A (0,0,0)
  2. B \(\left(\frac{5}{9}, \frac{35}{9}, \frac{-5}{3}\right)\)
  3. C \(\left(\frac{5}{3}, \frac{35}{3}, \frac{-5}{3}\right)\)
  4. D \(\left(\frac{5}{9}, \frac{35}{9}, \frac{-5}{9}\right)\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\left(\frac{5}{9}, \frac{35}{9}, \frac{-5}{9}\right)\)

Step-by-step Solution

Detailed explanation

Let \(G_1\) be the centroid of face \(A B D\). \(G_2\) be the centroid of face \(B C D\). \(G_3\) be the centroid of face \(A C D\).…