Show that the scalar product of two vectors obeys the commutative law.

(N/A) Let $\vec{A}$ and $\vec{B}$ be two vectors with an angle $\theta$ between them.
The scalar product (dot product) of $\vec{A}$ and $\vec{B}$ is defined as:
$\vec{A} \cdot \vec{B} = AB \cos \theta$
Since the product of scalar magnitudes $A$ and $B$ is commutative $(AB = BA)$,we can write:
$AB \cos \theta = BA \cos \theta$
By definition,$BA \cos \theta$ is the scalar product of $\vec{B}$ and $\vec{A}$:
$BA \cos \theta = \vec{B} \cdot \vec{A}$
Therefore,$\vec{A} \cdot \vec{B} = \vec{B} \cdot \vec{A}$.
This proves that the scalar product of two vectors obeys the commutative law.