Notations for Vector Division
While there are four standard ways of multiplying vectors and each has its own notation (\(\cdot\), \(\times\), \(\^\), \(\o\)), there is no generally-agreed-upon definition or notation for dividing vectors. That’s mostly because it’s not a thing. But there are times when I wish it was a thing. Or rather, there are too many times where a notion of division would be useful to ignore. There’s an operation which acts a lot like division, and which comes up more often than you might notice if you weren’t looking for it. And it does, in a sense, generalize scalar division. So why not?
This article describes what I would kinda like the notation \(\b{b} / \b{a}\) should mean. I’m writing it out primarily because I keep wanting to refer to it in other articles; this way I have something to link to instead of defining it inline each time. I don’t mean to claim that this “is” vector division. Rather it’s a thing that is sufficiently common that it makes sense to generalize the notation of division for.