In this note on space geometry, the Gram determinant is used for
expressing distances, vectors whose magnitude equals those distances and
best approximation points. Three cases are considered: distances from a
point to a line and to a plane and distances between two skew lines.
(Symbolic) determinants occur in the expressions of the feet of
perpendiculars and in the representation of the vectors materializing the
distances. Because best approximation problems often require the use of
subspaces, in order to solve the general cases of the proposed problems,
we make extensive use of the conjugacy principle much present in
Mathematics. The main purpose of this paper, focused on the resolution of
distance problems in tridimensional geometry, is to provide the
acquisition of spatial abilities through the proposed constructive approach.
The obtained results, which could be a starting point and give clues for
solving more advanced geometry problems, are applicable in several fields
of practical sciences, such as the Coordinate Metrology, for instance.
Moreover, this paper may be a window for coming across with a diversity
of scalar products.info:eu-repo/semantics/publishedVersio
