VAE operators for solving problems of vector objects formation

Paper describes a set of vector algebra operators extending its representation to what can be thought of as geometric operations. These operations are used solving orientation problems, problems of guidance and control definitions in a space as well as problems of positioning, contiguity and intersections of vector objects in their coordinate space.
Suggested operational set of vector motions helps with developing numerical algorithms aimed to be used for solving positional and orientational tasks in robotics. Furthermore, using the logic and semantics of clauses built with a language based on proposed set of geometric operators allows for efficient and generic non-coordinate descriptions of mutual special positions of objects in a space.
A set of geometric objects together with described system of operations which forms a Vector Algebra Extension (VAE) are also useful at semantic level descriptions in modern AI tasks.