ABSTRACT
Many geometric theorems deal with the interdependence of properties that hold between such objects. A point may lie on a line or on a circle, a circle and line may touch tangentially, two lines may enclose a certain angle, two points may be at a certain distance, etc. A geometric theorem is typically stated in a way where certain such relations (the hypotheses) imply another such relation (typically under the presence of certain non-degeneracy assumptions). Incidence geometry. In principle the algebra of meet $ meet $ and join $ join $ operations is very well suited to perform direct calculations in which three-dimensional vectors represent geometric points and lines. One crucial ingredient of such calculations comes from the fact that nested vector products can be reformulated as linear combinations of expressions involving geometric objects and determinants.
