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Scalar Triple Product

The Vector product

\begin{displaymath}[{\bf A},{\bf B},{\bf C}]\equiv {\bf A}\cdot ({\bf B}\times {...
..._2 & A_3\cr B_1 & B_2 & B_3\cr C_1 & C_2 & C_3\cr}\right\vert,

which yields a Scalar (actually, a Pseudoscalar).

The Volume of a Parallelepiped whose sides are given by the vectors ${\bf A}$, ${\bf B}$, and ${\bf C}$ is

V_{\rm parallelepiped} = \vert{\bf A}\cdot ({\bf B}\times {\bf C})\vert.

See also Cross Product, Dot Product, Parallelepiped, Vector Triple Product


Arfken, G. ``Triple Scalar Product, Triple Vector Product.'' §1.5 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 26-33, 1985.

© 1996-9 Eric W. Weisstein