About some properties of tetrahedron via vectors

Abstract

This contribution introduces the reader with some basic properties of the tetrahedron using the method of working with vectors as oriented segments. This approach is not widely used in teaching of the geometry in upper-secondary schools, although it is a useful mean how to develop a spatial thinking. It contributes to combining analytic and synthetic geometry into a one unit and in addition, it has wide applications in physics and in practice, too. Through the example of the existence of the selected centers of the tetrahedron we show how useful is working with vectors without the usage of the system of coordinates. By usage a connection between the tetrahedron in-scribed into a parallelepiped and with implementation of the operations with vectors, including scalar and vector product, as well as their geometric meaning, we derive the existence of gravity and orthocenter of the tetrahedron.