( xv) Moment of a Couple
( a) Two equal and unlike parallel forces whose lines of action are different are said to constitute a couple.
( b) Let P and Q be any two points on the lines of action of the forces – F and F, respectively.
The moment of the couple = PQ x F
Scalar Triple Product
If a, b, c are three vectors, then( a * b) * c is called scalar triple product and is denoted by [ a b c ].
∴ [ a b c ] =( a * b) * c
Geometrical Interpretation of Scalar Triple Product
The scalar triple product( a * b) * c represents the volume of a parallelepiped whose coterminous edges are represented by a, b and c which form a right handed system of vectors.
Expression of the scalar triple product( a * b) * c in terms of components a = a1i + a1j + a1k, b = a2i + a2j + a2k, c = a3i + a3j + a3k is