yours katarnak Suresh
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Scalar Triple Product
The scalar triple product of three vectors , , and is denoted and defined by
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
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(6)
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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 , , and is given by the absolute value of the scalar triple product
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(10)
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SEE ALSO: Cross Product, Dot Product, Parallelepiped, Vector Multiplication, Vector Triple Product
REFERENCES:
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.
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, 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: Scalar Triple Product
In mathematics, the triple product is a product of three vectors. The name "triple product" is used for two different products, the scalar-valued scalar triple product and, less often, the vector-valued vector triple product.