The aim of our research is to establish relationship between linearly independent vectors and the R3 Space The means for that are going to be taken from Balanced Ternary analysis e.g. triplets with entries (-1,0,1) This is not going to be any specific vector, for instance (-1,0,1) It’s going to be rather a Coordinate system with 8 quadrants and directional vectors The novelty of the proposed research lies in the fact that unlike traditional Cartesian system-vector basis our system uses 8 vectors which are at the same time a polyvector (Boas) We may define it as a multiple of the type:  ∑ (i=-1)^1∑ (j=-1)^1 ∑ (k=-1)^1〖(i,j,k)〗