MHT CET · Maths · Vector Algebra
The centroid of tetrahedron with vertices at \(A(-1,2,3), B(3,-2,1), C(2,1,3)\) and \(D(-1,-2,4)\) is
- A \(\left(\frac{3}{4}, \frac{-1}{4}, \frac{11}{4}\right)\)
- B \(\left(\frac{5}{4}, \frac{-3}{4}, \frac{7}{4}\right)\)
- C \(\left(\frac{-3}{4}, \frac{-1}{4}, \frac{11}{4}\right)\)
- D \(\left(\frac{-5}{4}, \frac{-3}{4}, \frac{-7}{4}\right)\)
Answer & Solution
Correct Answer
(A) \(\left(\frac{3}{4}, \frac{-1}{4}, \frac{11}{4}\right)\)
Step-by-step Solution
Detailed explanation
Centroid of tetrahedron
\(
\begin{aligned}
& \equiv\left(\frac{-1+3+2-1}{4}, \frac{2-2+1-2}{4}, \frac{3+1+3+4}{4}\right) \\
& \equiv\left(\frac{3}{4}, \frac{-1}{4}, \frac{11}{4}\right)
\end{aligned}
\)
\(
\begin{aligned}
& \equiv\left(\frac{-1+3+2-1}{4}, \frac{2-2+1-2}{4}, \frac{3+1+3+4}{4}\right) \\
& \equiv\left(\frac{3}{4}, \frac{-1}{4}, \frac{11}{4}\right)
\end{aligned}
\)
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