Open Access
Subscription Access
Unit Vector Relations via Direction Cosines
Conversion of a vector from a coordinate system to another is done via the dot product operation. Unit vector relationships have been either studied by the vector projection method or by a set of complex geometric relationship. Both of these conventional methods are rather lengthy & time-consuming and are moreover difficult to recall. In this paper, through a step by step approach employing direction cosines, the authors were able to find the unit vector conversions between the rectangular and the spherical system efficiently. A densely labelled graph showing all variable relations is required from which the results precipitate coincidentally.
Keywords
Cartesian, coordinate system, vector conversion, dot product, electromagnetism, rectangular, spherical, direction cosines, unit vector.
User
Font Size
Information
- Hayt, W.H., Buck, J.A. and Akhtar, Engineering Electromagnetics, 8th Ed., Tata McGraw-Hill.
- Sadiku, M., Elements of Electromagnetics, 6th Ed.. Oxford University Press.
- Serway, R. A., Physics for Scientists & Engineers with Modem Physics, 4th Ed., Saunders College Pub, Philadel-phia, USA.
- Stroud, K.A. and Booth, D., Engineering Mathematics, 7th Ed., Red Globe Press.
- A collection of materials for physics students and instructors, accessed in November 2021. https://www.cpp.edu/ ~ajm/materials/delsph.pdf
- Snyder, J.P., Map Projections: A Working Manual, Geological Survey (U.S.), Report Number1395,p.37,1987.
- Gauss, K.F., General Investigations of Curved Surfaces of 1827 and 1825, The Princeton University Library, Translated in 1902.
- Zahn, M., Electromagnetic Field Theory, MIT Open Course Ware, http://ocw. mit.edu, accessed in January 2022.
- Zahn, M., Electromagnetic Field Theory: A Problem Solving Approach, Malabar, F.L.: Krieger Publishing Company, 2003.
Abstract Views: 554
PDF Views: 265