TS EAMCET · Maths · Three Dimensional Geometry
If \(A(1,2,3), B(2,-3,1), C(3,2,-1)\) are three vertices of a tetrahedron \(\mathrm{ABCD}\) and \(\mathrm{G}\left(\frac{5}{2}, \frac{3}{2}, \frac{9}{4}\right)\) is its centroid then the point which divides GD in the ratio \(1: 2\) is
- A \((6,1,3)\)
- B \(\left(3, \frac{8}{3}, 3\right)\)
- C \(\left(\frac{1}{3}, \frac{2}{3}, 1\right)\)
- D \(\left(3, \frac{8}{3}, \frac{7}{2}\right)\)
Answer & Solution
Correct Answer
(D) \(\left(3, \frac{8}{3}, \frac{7}{2}\right)\)
Step-by-step Solution
Detailed explanation
Let the vertices be \(\mathrm{D}(a, b, c)\) \(\mathrm{G}\) is the centroid of the tetrahedron \(\mathrm{ABCD}\) then, \[ \mathrm{G}=\frac{\mathrm{A}+\mathrm{B}+\mathrm{C}+\mathrm{D}}{4} \] Here, \(\mathrm{A}(1,2,3), \mathrm{B}(2,-3,1), \mathrm{C}(3,2,-1)\) and…
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