@curious_mind I am not sure what you mean. Vectors are elements of a "vector space", which is defined in mathematics. $\mathbb{R}^n$ consisting of $n$-tuples with its defined operations of vector addition and scalar multiplication is a vector space. This vector space is used as a model for many vector quantities such as position, force, velocity, acceleration, and so on. It should be pointed out that many mathematical definitions have taken their inspiration from nature ("physical world").