Usage of the word "vi"

In the game League of Legends, the character Vi is known for her violent, aggressive, fight-loving nature, and isn't shy about expressing it. When asked what her name is short for, she has a different response each time, with each relating to this nature.

"Vi? Stands for Violence!!"
"Vi? Stands for Vice!"
"Vi? Heh... stands for Vicious!"

Beyond being a humorous joke, is the fact that these words have a similar theme more than a coincidence? Is vi a root word or prefix that has some meaning which causes this relation? Are there other words that begin with vi- that also fit this theme?

Solution 1:

Vi is proper Latin, and it means "with violence, violently", the ablative of vis, "force, violence", from Proto-Indo-European *u̯i-, with similar meaning, and probably related to various other roots and their reflexes. Words like vir "man", virtus "might, virtue", violo "violate" (all senses) come from *vi-.

If you scribble v.c. next to your signature on a contract, it is said that you can thereby prove that you signed under duress, where v.c. stands for vi coactus, "coerced by violence". Presumably, illiterate criminals won't notice at the time of signing.

English vice and vicious come from Latin vitium "fault, vice", which comes from another, apparently unrelated Proto-Indo-European root *u̯i- meaning "apart, separate" (a vice may be errant from the right path?). This is probably related to evito "to avoid", related to English inevitable.

Solution 2:

Not really.

Vicious is indeed related to vice and originally was the adjective form of it. But that "originally" goes back to the Latin words from which they each derive, and the meaning has shifted since.

Violence is completely different, coming from the latin violare, rather than vitium as vice and, ultimately, vicious does.

So while there is some degree of relationship between two of the words you give, there isn't between them and the first and it so it wouldn't seem to be something the writers where deliberately keying off.