Up to now, there is a long time problem that dot product has no corresponding division. In order to solve this problem, in this paper, indefinite dot quotients are introduced as extensive inverse operations of dot products, which solve the problem in 3-dimensional space that the quotient of a number and a vector on dot product does not exist from another angle. Some basic properties, and some expected operation properties, and two forms of geometric expressions and six coordinate formulas of indefinite dot quotients are presented.
References
[1]
Joag, P.S. (2016) An Introduction to Vectors, Vector Operators, and Vector Analysis. Cambridge University Press, Cambridge.
https://doi.org/10.1017/9781316650578
https://www.doc88.com/p-59616596439664.html
[2]
Weatherburn, C.E., Came, M.A. and Sydney, D.S. (1921) Elementry Vector Analysis with Application to Geometry and Physics. G. Bell and Sons, ltd., London.
Lengyel, E. (2012) Mathematics for 3D Game Programming and Computer Graphics. 3rd Edition, Course Technology, Boston.
[5]
Kang, R.J., Lovász, L., Müller, T. and Scheinerman, E.R. (2011) Dot Product Representations of Planar Graphs. In: Brandes, U., Cornelsen, S., Eds., Graph Drawing. GD 2010. Lecture Notes in Computer Science. Springer, Berlin, Heidelberg.
https://doi.org/10.1007/978-3-642-18469-7_26
[6]
Lopes, A.R. and Constantinides, G.A. (2010) A Fused Hybrid Floating-Point and Fixed-Point Dot-Product for FPGAs. Reconfigurable Computing: Architectures, Tools and Applications, 6th International Symposium, ARC 2010, Bangkok, Thailand, March 17-19 2010. Springer.
[7]
Massey, W.S. (1983) Cross Products of Vectors in Higher Dimensional Euclidean Spaces. The American Mathematical Monthly, 90, 697-701.
https://doi.org/10.1080/00029890.1983.11971316
[8]
Silagadze, Z.K. (2002) Multi-Dimensional Vector Product. Journal of Physics A: Mathematical and General, 35, 4949. https://doi.org/10.1088/0305-4470/35/23/310
[9]
Wang, J.X. and Cheng, L. (2022) Indefinite cross Divisions of Vectors in Natural Space. Open Access Library Journal, 9, Article e9415.
https://doi.org/10.4236/oalib.1109415
[10]
Galbis, A. and Maestre, M. (2012) Vector Analysis versus Vector Calculus. Springer, New York. https://doi.org/10.1007/978-1-4614-2200-6
