The vertices of the tetrahedron of V-ABC are $V (4, 5, 1), A (0, - 1, - 1), B (1, 2, 3) a n d C (4, 4, 4)$ . Find its volume.

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Solution

$\begin{matrix} \to a = \to V A, \to b = \to V B, \to C = \to V C \Rightarrow \to a = (- 3, - 6, - 2) \end{matrix}$
$\begin{matrix} \to b = (- 3, - 3, 2) \to c = (0, - 1, 3) \end{matrix}$
$V = \frac{1}{6} ⎡ ⎢ ⎣ \begin{matrix} - 3 & - 6 & - 2 - 3 & - 3 & 2 0 & - 1 & 3 \end{matrix} ⎤ ⎥ ⎦$
$\begin{matrix} = \frac{1}{6} | - 39 | = \frac{39}{6} = \frac{13}{2} {unit}^{3} \end{matrix}$

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