Question

How to determine if vectors are parallel?

Answer 1

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 $\pi$.