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# Find the volume of the tetrahedron with vertices (0,0,0), (3,0,0), (0,5,1), (2,0,5)

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Find the volume of the tetrahedron with vertices (0,0,0), (3,0,0), (0,5,1), (2,0,5)

May 14, 2022

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Let O = (0, 0, 0), A = (3, 0, 0), B = (0, 5, 1), and C = (2, 0, 5).

Volume of tetrahedron = $$\renewcommand{\vec}{\overrightarrow} \dfrac16\left|\vec{OA} \cdot \left(\vec{OB} \times \vec{OC}\right)\right|$$ = $$\dfrac 16 \begin{vmatrix}3&0&0\\0&5&1\\2&0&5\end{vmatrix}$$ = 25/2 cubic units.

May 14, 2022