Direction as a Form of Energy: A Conceptual and Mathematical Link between Vectors, Scalars, and Particle Dynamics

Sandeep Singh*
Lecturer and Independent Researcher.
Periodicity:July - December'2025

Abstract

This paper investigates the conceptual and mathematical relationship between direction, energy, vector quantities, and scalar quantities in physical systems. Unlike a purely geometric interpretation, direction is treated as an energy- dependent outcome governed by environmental conditions and force fields. Using vector mechanics and vector calculus-specifically gradients, divergence, curl, and line integrals-we demonstrate how directional behavior emerges from scalar energy distributions and how scalar energy values are obtained from vector interactions. This manuscript presents a structured and mathematically justified framework for researchers.

Keywords

Direction, Energy, Vector Calculus, Scalar Fields, Particle Dynamics.

How to Cite this Article?

Singh, S. (2025). Direction as a Form of Energy: A Conceptual and Mathematical Link between Vectors, Scalars, and Particle Dynamics. i-manager’s Journal on Physical Sciences, 4(2), 1-5.

References

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