A note on dual third order Jacobsthal vectors

TL;DR

This paper introduces dual third order Jacobsthal and Jacobsthal-Lucas numbers and vectors, exploring their properties, identities, and geometric applications in dual space.

Contribution

It defines new dual Jacobsthal vectors and derives their properties, identities, and geometric relations, expanding the mathematical understanding of these dual number systems.

Findings

Derived quadratic identities and Binet formulas.

Established summation and norm properties.

Explored geometric applications in dual space.

Abstract

Dual third order Jacobsthal and dual third order Jacobsthal-Lucas numbers are defined. In this study, we work on these dual numbers and we obtain the properties e.g. some quadratic identities, summation, norm, negadual third order Jacobsthal identities, Binet formulas and relations of them. We also define new vectors which are called dual third order Jacobsthal vectors and dual third order Jacobsthal-Lucas vectors. We give properties of these vectors to exert in geometry of dual space.