I am learning multivariate calculus, which makes me questioning my understanding of a vector. Can someone please give me an intuition for the direction of a vector in a general abstract term?
For example, what does the direction of the vector (1,2,-3,-4) mean? I tend to think of it as a "movement" such that from a given point, the 1st dimension changes by 1, the 2nd by 2, etc in some same amount of "time". This feels a bit unsettled to me since I have to use the mysterious notation of "time", which pops out from nowhere.
Thank you!