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)〗