Mixed Product Definition

Mixed product otherwise referred to as scalar triple product, triple scalar product and box product is a method of multiplying three 3-dimensional vectors, usually euclidean vectors in which the resulting product is a scalar. It is the dot product of one of the vectors with the cross product of the other two. The absolute value of a mixed product is the volume of the parallelepiped formed by the three vectors. The mixed product of vectors u, v, and w is u∙(v×w). 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.