Triple Scalar Product

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triple scalar product

[′trip·əl ′skā·lər ‚präd·əkt]
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Triple Scalar Product


The triple scalar product of the vectors a, b, and c is the result of the scalar multiplication of the first of these vectors by the vector product of the second and third vectors: a·(b × c). It is often written [abc] or (abc).

The numerical value of the triple scalar product is equal to the volume of the parallelepiped of which the vectors a, b, and c are coterminal sides; the volume is taken with a plus sign if a, b, and c are oriented in the same way as the unit coordinate vectors i, j, and k, and with a minus sign otherwise. If a, b, and c are written in the forms a = a1 i + a2 j + a3k, b = b1i + b2j + b3 k, and c = c1 i + c2 j + c3 k, then the triple scalar product is the determinant of the coefficients of i, j, and k. A triple scalar product remains unchanged under a cyclic permutation of a, b, and c; in the case of a noncyclic permutation, the product changes in sign.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.