Cartesian Parallellism, $\underline{a} \neq \underline{0}$:

\[
  \underline{a} \parallel \underline{b}
  \quad \Leftrightarrow \quad 
  \exists k \in \mathbb{R}:~\underline{a}=k\underline{b}
  \quad \Leftrightarrow \quad 
  Det(\underline{a},\underline{b})=0
\]