Are vectors abelian?

Are vectors, in the mathematical context often encountered in physics and engineering, truly abelian? This question delves into the realm of algebraic structures, where abelian groups play a pivotal role. Abelian groups are characterized by the commutative property of their operation, meaning that the order in which elements are combined does not affect the result. In the case of vectors, do they adhere to this same principle? Or are they governed by different rules that Render the notion of them being abelian inapplicable? Let's delve deeper and explore the intricacies of vector operations and their compatibility with the abelian group framework.