Scalar Triple Product

Scalar Triple Product

If ,,are three vectors then( x ). is called the scalar triple product of these three vectors and is conventionally represented by [ ]. It is also known as box product. Geometrically it denotes the volume of a parallelepiped whose conterminous edges are represented by

Properties of Scalar Triple Product

(a)

(b)

(c) If k is a scalar then; also

(d) If

(e) The value of scalar triple product, if two of its vectors are equal is zero

i.e. .

(f) Also

(g) The volume of a tetrahedron whose adjacent sides are represented by the vectors  . andis The position vectors of the centroid of a tetrahedron whose vertices are ,, and is .

(h) The volume of a triangular prism whose adjacent sides are represented by .

(i) If , then ,and are coplanar

(j) Three vectors form a right handed or left handed system according as

(k)