On possibility of vector product determination of two vectors in multidimensional space

Author(s):  I.P. Popov, Kurgan state university, Kurgan, Russia, ip.popow@yandex.ru

Issue:  Volume 49, №27

Rubric:  Mathematics

Annotation:  The aim of the paper is to define the vector product of two vectors c = [a, b] in n-dimensional Euclidean space for n > 3. Orthonormal bases are used in this paper. It is proved that for two linearly independent vectors a and b in Rn exists their vector product. We introduce the notion of m-splitting and symmetric m-splitting of basis vectors, by which is meant a transformation Rn in Rn+m–1 by replacing ei by m vectors 1,..., ,..., i ij im eee orthogonal to each other and to 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 Rn . A condition is established in accordance with which the vector product c = [a, b] in Rn lies on one line with the projection of the sum of the basis vectors to the (n – 2)-plane perpendicular to the vectors a and b.

Keywords:  vector product, multidimensional space, basis, splitting.

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