No, $$\vec{v_1}$$ and $$\vec{v_2}$$ are not unit vectors, they are of arbitrary length.

TheSobserver is considering the velocity vectors:

$$\begin{align}The units vectors of $$\vec{v_1}$$ and $$\vec{v_2}$$ are identical, so the

\vec{v_1} &= (0,v_1) \\

\vec{v_2} &= (0,v_2)

\end{align}$$Sobserver concludes that $$\vec{v_1}$$ and $$\vec{v_2}$$ are parallel.

Is that correct?

No, it isn't correct. You have a class of (parallel) vectors, $$(0,v_i), 1<i<n$$. None of these vectors is a unit vector. The representative of this class is the

**unit vector**$$(0,1)$$. When judging vector parallelism, you need to stop using the members of the class and start using the class representative. This way, the notion of parallelism is independent of vector norm (length).