Vector Quantity as Scalar Product of Unit Vector Quantity

Theorem
Let $\mathbf a$ be a vector quantity.

Then:
 * $\mathbf a = \size {\mathbf a} \mathbf {\hat a}$

where:
 * $\size {\mathbf a}$ denotes the magnitude of $\mathbf a$
 * $\mathbf {\hat a}$ denotes the unit vector in the direction $\mathbf a$.