( 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