Scalar Triple Product - From Wolfram MathWorld

Scalar Triple Product.
where denotes a dot product, denotes a cross product, denotes a determinant, and , , and are components of the vectors , , and , respectively. The scalar triple product is a pseudoscalar (i.e., it reverses sign under inversion). The scalar triple product can also be written in terms of the permutation symbol as.
where Einstein summation has been used to sum over repeated indices.
Additional identities involving the scalar triple product are.
The volume of a parallelepiped whose sides are given by the vectors , criptografia de cópia , and is given by the absolute value of the scalar triple product.
See also.
Explore with Wolfram|Alpha.
More things to try:
References.
Arfken, G. "Triple Scalar Product, Triple Vector Product." §1.5 in Mathematical Methods for Physicists, If you have any sort of inquiries relating to where and the best ways to use criptografia de cópia, you could contact us at our internet site. 3rd ed. Orlando, FL: Academic Press, pp. 26-33, 1985. Aris, R. "Triple Scalar Product." §2.34 in Vectors, Tensors, and the Basic Equations of Fluid Mechanics. New York: Dover, pp. 18-19, 1989. Griffiths, D. J. Introduction to Electrodynamics. Englewood Cliffs, NJ: Prentice-Hall, p. 13, 1981. Jeffreys, H. and Jeffreys, B. S. "The Triple Scalar Product." §2.091 in Methods of Mathematical Physics, 3rd ed. Cambridge, England: Cambridge University Press, copiar criptografia de comércio pp. 74-75, 1988. Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, p. 11, 1953.
Referenced on Wolfram|Alpha.
Cite this as:
Subject classifications.
About MathWorld MathWorld Classroom Send a Message MathWorld Book wolfram.com 13,876 Entries Last Updated: Thu Feb 9 2023 ©1999–2023 Wolfram Research, Inc. Terms of Use wolfram.com Wolfram Language Mathematica Wolfram Demonstrations Wolfram for Education.