Find the volume of the tetrahedron with the vertices $P(1,1,1)$, $Q(1, 2, 3)$, $R(3, 1, 2)$, and $S(2, 3, 1)$.
Finding the volume of the tetrahedron.
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geometry
volume
1 Answers
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Volume of a tetrahedron is $\dfrac13 \times \text{Base area} \times \text{height}$ If the vertices are $\vec{v_1},\vec{v_2},\vec{v_3},\vec{v_4}$, then the volume is given by $\left \vert \dfrac{(\vec{v}_2 - \vec{v}_1) \cdot \left((\vec{v}_3 - \vec{v}_1) \times (\vec{v}_4 - \vec{v}_1) \right)}6 \right \vert$ where $\vec{a} \cdot \vec{b}$ denotes the inner/dot product, and $\vec{a} \times \vec{b}$ denotes the cross product.
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0Oh the magic of Math. i$n$teresting, thank you. – 2012-10-30