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.
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I. Todhunter, A treatise on plane coordinate geometry, Macmillan & Co., Cambridge, 1955. [2] A. Baker, Analytical geometry for beginners, W. J. Gage & Company Ltd., Toronto, 1905. [3] S.N. De, (1998). Higher Secondary Mathematics, Vol.-II, Chhaya Prakashani, Calcutta, India, 1998. [4] K.C. Nag, Higher Mathematics, Vol. – II, Calcutta Book House (P) Ltd, Calcutta, India, 1997. [5] M. R. Spiegel, Schaum’s outline of theory and problems of vector analysis and introduction to tensor analysis, Schaum’s Outline Series, McGraw-Hill, New York, 1990.
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