# Volume of a tetrahedron and a parallelepiped Calculator

## Calculates the volumes of a tetrahedron and a parallelepiped given four vertices.

vertex A (
 , , )
vertex B (
 , , )
vertex C (
 , , )
vertex D (
 , , )

volume Vp
 of a parallelepiped
volume Vt
 of a tetrahedron
 $\normal Parallelepiped\ and\ Tetrahedron\\\vspace{5}(1)\ V_p=\vec{AD}\cdot(\vec{AB}\times\vec{AC})\\{\small \hspace{18}= (x_4-x_1)[(y_2-y_1)(z_3-z_1)-(z_2-z_1)(y_3-y_1)] \\\hspace{18}+(y_4-y_1)[(z_2-z_1)(x_3-x_1)-(x_2-x_1)(z_3-z_1)] \\\hspace{18}+(z_4-z_1)[(x_2-x_1)(y_3-y_1)-(y_2-y_1)(x_3-x_1)]} \\\vspace{5}(2)\ V_t={\large\frac{V_p}{6}}\\$

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