AP EAMCET · Maths · Three Dimensional Geometry
Let \(\mathrm{ABCD}\) be a tetrahedron in which the coordinates of each of its vertices are in arithmetic progression with same common difference. If the centroid \(\mathrm{G}\) of the tetrahedron is \((2,3, \mathrm{k})\), then the distance of \(\mathrm{G}\) from the origin is
- A \(\sqrt{38}\)
- B \(7\)
- C \(\sqrt{22}\)
- D \(\sqrt{29}\)
Answer & Solution
Correct Answer
(D) \(\sqrt{29}\)
Step-by-step Solution
Detailed explanation
Let coordinates of vertices of tetrahedron are \(\begin{aligned} & A\left(a_1-d, a_1, a_1+d\right) ; B\left(a_2-d, a_2, a_2+d\right) ; \\ & C\left(a_3-d, a_3, a_3+d\right) \text { and } D\left(a_4-d, a_4, a_4+d\right) \end{aligned}\) Centroid \(=(2,3, k)\)…
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