### Scientific Research and Essays

• Abbreviation: Sci. Res. Essays
• Language: English
• ISSN: 1992-2248
• DOI: 10.5897/SRE
• Start Year: 2006
• Published Articles: 2758

## A new quaternion: Unit vector division quaternion

Department of Civil Engineering, Kocaeli University, Kocaeli, Turkey.
Email: [email protected]

•  Accepted: 16 July 2010
•  Published: 04 August 2010

Abstract

It is well known that, quaternion algebra allows the defining division of 3-D vectors. Division of vectors has many applications in applied mathematics and mechanics. However, indicial notation is widely used in the branches mentioned above. It is shown in this paper that division of orthonormal vectors can be conveniently handled by a simple operator. This operator can be used in the division of two arbitrary vectors and allows the expression of vector division using indicial notation. This new operator, which is a quaternion itself, can be also used in expressing quaternion product of two vectors, and the derivative of a vector with respect to a vector.

Key words: Quaternion, vector quaternions, Einstein’s summation convention.