[Math] how to calculate if two vectors are ‘parallel’

Question

We know we can check if two vectors are 'orthogonal' by doing an inner product.

$a*b=0$

tells us that these two vectors are orthogonal

here comes the question:

if there a way to compute if they are 'parallel'? i.e., they are pointing at the same direction.

Answer 1

Two parallel vectors $a$ and $b$ will have a null cross product: $$a\times b=0\iff a\parallel b.$$