I'm only 4 weeks into my first college-level physics course, so this is a very elementary question.
Also, in asking this question, I'm just playing devil's advocate in order to better understand the historical motivation for the use of vectors to describe physical phenomena. I'm not actually proposing we stop using them. :) So, please don't bash me for asking this innocent question.
As I was reading my textbook today, I wondered why vectors were invented and are still useful today. I have a little experience with them from my Trigonometry course, but they've always seemed a bit counterintuitive to me, as a tool for modeling and calculating.
What are the benefits of representing magnitude and direction (or other related values) with a single variable, instead of treating them as separate values with distinct variables?
What are the drawbacks (aside from increased complexity), if any, of using vectors instead of performing calculations and building models in which the speed and direction of a moving object (for example) are treated as distinct values with a distinct variable for each quantity?