One could use the relation
\(\mathbf a\cdot\mathbf b=\|\mathbf a\|\|\mathbf b\|\cos\theta\)
where \(\mathbf a,\mathbf b\) are two vectors, \(\|\mathbf a\|\) denotes the norm of that vector, and \(\theta\) is the angle between the two vectors.
Then the two vectors will be parallel if \(\theta=0\) or \(\pi\).
