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AP EAMCET · Maths · Vector Algebra

Consider the tetrahedron with the vertices \(\mathrm{A}(3,2,4)\), \(\mathrm{B}\left(x_1, y_1, 0\right), \mathrm{C}\left(x_2, y_2, 0\right), \mathrm{D}\left(x_3, y_3, 0\right)\). If the triangle BCD is formed by the lines \(y=x, x+y=6\) and \(\mathrm{y}=1\), then the centroid of the tetrahedron is

  1. A \(\left(\frac{9}{4}, \frac{7}{4}, 1\right)\)
  2. B \(\left(\frac{11}{4}, \frac{5}{4}, 1\right)\)
  3. C \(\left(3, \frac{7}{4}, 1\right)\)
  4. D \((3,2,1)\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\left(3, \frac{7}{4}, 1\right)\)

Step-by-step Solution

Detailed explanation

\(\mathrm{A}(3,2,4), \mathrm{B}\left(x_1, y_1, 0\right), \mathrm{C}\left(x_2, y_2, 0\right), \mathrm{D}\left(x_3, y_3, 0\right)\) \(\triangle \mathrm{BCD}\) is formed by lines \(y=x, x+y=6, y=1\) \(\therefore\) Vertices of BCD are D \((1,1), \mathrm{C}(3,3), \mathrm{D}(5,1)\)…