The volume of the tetrahedron whose vertices are $(0, 1, 2), (3, 0, 1), (4, 3, 6)$ and $(2, 3, 2)$ is equal to

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Solution

Given, $(0, 1, 2), (3, 0, 1), (4, 3, 6), (2, 3, 2)$
The required volume $= \frac{1}{6} | [A B A C A D] |$ .
But $A B = 3 \to i - \to j - \to k; A C = 4 \to i + 2 \to j + 4 \to k; A D = 2 \to i + 2 \to j$
So, volume of the tetrahedron $= \frac{1}{6} | ∣ ∣ ∣ ∣ \begin{matrix} 3 & - 1 & - 1 4 & 2 & 4 2 & 2 & 0 \end{matrix} ∣ ∣ ∣ ∣ | = 6$

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