Many sources define vectors to be geometric objects that have length and direction. I don't think this is rigorous enough a definition because I have learnt from other sources that there are other things besides vectors which have direction and magnitude. Also, a physics book that I use says that having length and direction is a necessary condition but not sufficient as vectors also need to satisfy the laws of vector addition.
Is a vector simply an arrow in space?
Is there a reason as to why so many physical quantities are vectors?
These are some questions I hope to be able to answer once I know what a vector actually is. So it would be great if you could shed some light on these questions too.
