The curriculum of our university reflects the development of the exact natural sciences in a lecture on the fundamental ideas of modern physics, which organically concludes the instruction in Technical Electrodynamics. Knowledge of vectors is indispensable for the study of Theoretical Electricity. Since this principle has long been recognized, there is hardly a modern textbook in this discipline that does not begin with an overview of vector calculus. Among them, there is certainly no shortage of masterful representations; it is not sufficient to rely on just one of them. This document aims to demonstrate through its existence that the previously common foundation of vector theory has become too narrow for modern natural science: in its field, it is necessary to free oneself mentally from the constraints of three-dimensional perception.