Abstract
The aim of the paper is to define the vector product of two vectors c =[a, b] in four-dimensional Euclidean space. We introduce the notion of m-splitting and symmetric m-splitting of basis vectors, by which is meant the transformation of R^n into R^(n+m–1) by replacing e_i by m vectors e_i1,…,e_ij,…,e_im orthogonal to each other and all other basis vectors of the original basis. The inverse problem is solved in some way-for a known vector product the definition of the coordinates of all three vectors in R^n. A condition is established in accordance with which the vector product c =[a, b] in R^4 lies on one line with the projection of the sum of the basis vectors to the 2-plane perpendicular to the vectors a and b. The results of the work can be used to solve multidimensional physics and engineering problems.
Keywords
Gradient, function, partial derivative, integral, variable.
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