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Tetrahedron

Find the volu...

Question

Find the volume of the tetrahedron whose co-terminals edges are $2 ˆ i + 6 ˆ j + 4 ˆ k, ˆ i + ˆ j + 2 ˆ k 3 ˆ i + ˆ j + 3 ˆ k$

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Solution

$\begin{matrix} a = 2^i + 6^j + 4^k b =^i +^j + 2^k c = 3^i +^j + 3^k (a b c) = ∣ ∣ ∣ ∣ \begin{matrix} 2 & 6 & 4 1 & 1 & 2 3 & 1 & 3 \end{matrix} ∣ ∣ ∣ ∣ = 2 (3 - 2) - 6 (3 - 6) + 4 (1 - 3) = 2 + 18 - 8 = 12 u n i t \end{matrix}$

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