TS EAMCET · Maths · Straight Lines
\(\mathrm{A}(1,1,1), \mathrm{B}(1,-4,3), \mathrm{C}(2,-2,0)\) and \(\mathrm{D}(8,1,4)\) are the vertices of a tetrahedron. \(\mathrm{G}_1, \mathrm{G}_2, \mathrm{G}_3\) and \(\mathrm{G}_4\) are the centroids of the faces \(\mathrm{ABC}, \mathrm{BCD}, \mathrm{CDA}\) and \(\mathrm{DAB}\). Then the centroid of the tetrahedron having \(\mathrm{G}_1, \mathrm{G}_2, \mathrm{G}_3, \mathrm{G}_4\) as its vertices is
- A \((12,-4,8)\)
- B \(\left(4, \frac{-4}{3}, \frac{8}{3}\right)\)
- C \(\left(2, \frac{-2}{3}, \frac{4}{3}\right)\)
- D \((3,-1,2)\)
Answer & Solution
Correct Answer
(D) \((3,-1,2)\)
Step-by-step Solution
Detailed explanation
Given vertices \(\mathrm{A}(1,1,1), \mathrm{B}(1,-4,3), \mathrm{C}(2,-2,0)\) and \(\mathrm{D}(8,1,4)\). Centroid of \(\triangle \mathrm{ABC}\) is \(\mathrm{G}_1=\left(\frac{1+1+2}{3}, \frac{1-4-2}{3}, \frac{1+3+0}{3}\right)\)…
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