AP EAMCET · Maths · Vector Algebra
A new tetrahedron is formed by joining the centroids of the faces of a given tetrahedron \(O A B C\). Then the ratio of the volume of the new tetrahedron to that of the given tetrahedron is
- A \(\frac{3}{25}\)
- B \(\frac{1}{27}\)
- C \(\frac{5}{62}\)
- D \(\frac{1}{162}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{27}\)
Step-by-step Solution
Detailed explanation
Let the position vectors of the vertices of tetrahedron \(O A B C\) are \(\mathbf{O A}=\mathbf{a}, \mathbf{O B}=\mathbf{b}\) and \(\mathbf{O C}=\mathbf{c}\) So, volume of tetrahedron \(O A B C=\frac{1}{6}[\mathbf{a} \mathbf{b ~ c}]\) Now, position vectors of vertices of new…
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