<s>[INST] How do I know if two vectors with $n$ components are parallel? How do I know if two vectors with $n$ components are parallel?
For example 
$$\begin{pmatrix}5\\2\\1\\3\\4\end{pmatrix} \text{, and } \begin{pmatrix}4\\1\\2\\3\\6\end{pmatrix}.$$
 [/INST] Put them together like: $$\begin{pmatrix} 5 & 4 \\ 2 & 1 \\ 1 & 2 \\ 3 & 3 \\ 4 & 6\end{pmatrix},$$
or in rows. If one of the $2 \times 2$ determinants there is non-zero, they're not parallel. They are not parallel because, for example, $\left|\begin{matrix} 5 & 4 \\ 2 & 1\end{matrix}\right| = -3 \neq 0$.
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