Generalize min-max scaling to vectors

I am combining several vectors, where each vector is a certain kind of embedding of some object. Since each embedding is very different (some have all components between $[0, 1]$ some have components in the range of around 60 or 70 etc.) I want to rescale the vectors before combining them. I thought about using something like min-max rescaling, but I'm not sure how to generalize it to vectors. I could do something of the sort - $\frac{v-|v_{min}|}{|v_{max}|-|v_{min}|)}$ but I don't think it makes much sense. Is there some generalization of min-max scaling for vectors, or generalization of some other kind of scaling?