Triple scalar product

From Glossary of Meteorology



triple scalar product

The scalar A · (B × C) written (ABC) or [ABC], where A, B, and C are any three vectors.

The dot denotes a scalar product and the cross a vector product. When A, B, and C are written in terms of their components along the x, y, and z axes of the rectangular Cartesian coordinates, that is, A = a1i + a2j + a3k, B = b1i + b2j + b3k, and C = c1i + c2j + c3k, the triple scalar product is the determinant
ams2001glos-Te43
Any cyclic change among the vectors in a triple product does not alter its value.


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