An ordinary number that does not change when the coordinate frame changes is called a scalar. Multiplication of a vector by a scalar rescales the vector by multiplying each of its components as a special case of this rule:
Note well that the vector components are themselves scalars. Indeed, we build a vector in the first place by taking a unit vector (of length one, ``pure direction'') and scaling it by its component length, e.g. , and then summing the vectors that make up its components!
The multiplication of a vector by a scalar is commutative: