Use of tangent and normal vectors for the derivation of equations of tangent and normal
Keywords:
cartesian coordinate geometry, vector algebra, dot product, cross product, rectangular unit vectors, gradient of a scalar point functionAbstract
Remaining within the frame work of vector algebra and vector calculus, this paper makes use of the tangent and normal vectors to a given curve at a given point on it for the derivation of the equations of tangent and normal to the curve at that point. The techniques of derivation offered are generalized, simple and straight forward. Furthermore, unlike the traditional techniques, the present scheme increases the range of applicability of one of the fundament concepts of vector calculus (namely, gradient of a scalar point function) as well. As a result, this contribution must have educational value and it will enrich and sophisticate the traditional literature thereby enhancing the same as well.
Downloads
References
Baker, A. (1905). Analytical geometry for beginners, W. J. Gage & Company Ltd., Toronto.
Candela-Munoz, J. L., & Rodríguez-Gámez, M. (2023). Active methodologies in mathematics learning. International Journal of Physics and Mathematics, 6(1), 45-52. https://doi.org/10.21744/ijpm.v6n1.2226
De, S. N. (1998). Higher Secondary Mathematics, Vol.-II, Chhaya Prakashani, Calcutta, India, 1998.
Liu, F., Xu, G., Liang, L., Zhang, Q., & Liu, D. (2016). Minimum zone evaluation of sphericity deviation based on the intersecting chord method in Cartesian coordinate system. Precision Engineering, 45, 216-229. https://doi.org/10.1016/j.precisioneng.2016.02.016
Mikhalev, A., & Oseledets, I. V. (2018). Rectangular maximum-volume submatrices and their applications. Linear Algebra and its Applications, 538, 187-211. https://doi.org/10.1016/j.laa.2017.10.014
Moon, Y. M., & Kota, S. (2002). Automated synthesis of mechanisms using dual-vector algebra. Mechanism and Machine Theory, 37(2), 143-166. https://doi.org/10.1016/S0094-114X(01)00073-8
Nag, K. C. (1997). Higher Mathematics, Vol. – II, Calcutta Book House (P) Ltd, Calcutta, India.
Spiegel, M. R. (1974). Schaum's outline of theory and problems of vector analysis and an introduction to tensor analysis. New York, USA: McGraw-Hill.
Todhunter, I. (2023). A treatise on plane co-ordinate geometry. BoD–Books on Demand.
Wang, D., Wang, J., & Wu, J. (2018). Superconvergent gradient smoothing meshfree collocation method. Computer Methods in Applied Mechanics and Engineering, 340, 728-766. https://doi.org/10.1016/j.cma.2018.06.021
Yamanaka, N., Ogita, T., Rump, S. M., & Oishi, S. I. (2008). A parallel algorithm for accurate dot product. Parallel Computing, 34(6-8), 392-410. https://doi.org/10.1016/j.parco.2008.02.002
Published
How to Cite
Issue
Section
Copyright (c) 2024 International journal of physics & mathematics
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Articles published in the International Journal of Physics & Mathematics (IJPM) are available under Creative Commons Attribution Non-Commercial No Derivatives Licence (CC BY-NC-ND 4.0). Authors retain copyright in their work and grant IJPM right of first publication under CC BY-NC-ND 4.0. Users have the right to read, download, copy, distribute, print, search, or link to the full texts of articles in this journal, and to use them for any other lawful purpose.
Articles published in IJPM can be copied, communicated and shared in their published form for non-commercial purposes provided full attribution is given to the author and the journal. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
