scalar (dot) product If there are two vectors a and b then the scalar product of a and b, written as a.b (a dot b) is defined as,

a.b = a b cosq (s1)

where a is the magnitude of a, and b the magnitude of b. q is the smaller angle between the two vectors, with initial points of the two vectors coinciding. The value of the scalar product is a scalar, a real number that is independent of Cartesian coordinates system in space. Example, work.