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BAC-CAB Identity

The vector triple product identity

Ax(BxC)=B(A·C)-C(A·B).

This identity can be generalized to n dimensions,

a_2x...xa_(n-1)x(b_1x...xb_(n-1))=(-1)^(n+1)|b_1 ... b_(n-1); a_2·b_1 ... a_2·b_(n-1); | ... |; a_(n-1)·b_1 ... a_(n-1)·b_(n-1)|.

See also

Vector Triple Product

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References

Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, p. 29, 1985.Aris, R. Vectors, Tensors, and the Basic Equations of Fluid Mechanics. New York: Dover, p. 19, 1989.Bronshtein, I. N. and Semendyayev, K. A. Handbook of Mathematics, 3rd ed. New York: Springer-Verlag, p. 519, 1998.Griffiths, D. J. Introduction to Electrodynamics. Englewood Cliffs, NJ: Prentice-Hall, p. 13, 1981.Marsden, J. E. and Tromba, A. J. Vector Calculus, 2nd ed. New York: W. H. Freeman, p. 39, 1981.Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, p. 114, 1953.

Referenced on Wolfram|Alpha

BAC-CAB Identity

Cite this as:

Weisstein, Eric W. "BAC-CAB Identity." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BAC-CABIdentity.html

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