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