Can we make curvy vectors? Or to put it another way: Instead of one straight direction, can the direction be round(or something like that)? Thanks
No. Direction can't be round but the path on which you are moving that can be round. And you want to know the direction in this round path you have to just joined the initial and final point and you will get the direction (means displacement vector).
We do have things like parametric equations which have a set direction and can curve through space, but they are not vectors, but more equations that could describe the exact path that say, a WWII era plane took while dogfighting. They can be set up as 3 equations, each describing a single dimension(x, y, or z) which all rely on a single variable, often "t".