Scalar or dot products of vectors, as they are called in the solutions, have the following important properties: The commutative law says that a.b = b.a = |a|.|b|.cos is true for any two given vectors. For any two vectors, a and b, this is true: (d.a). (e.b) = (d.b). (e.a) = de a.b. The square of the magnitude of a vector is the dot product, or scalar product, of that vector with itself. i.e. a.a = a2. The distributive law is shown by the dot product or scalar product of the given vectors. This means that a.(b + c) = a.b + a.c.