We can define the distance from a point P to a line r as the smallest of the distances from the point P to the infinite points on the line r. To determine this distance must obtain the line perpendicular to the line r from the point P and get their point of intersection I. The distance d from P to R is the minimum distance from this point to the line r.
This problem can have two different approaches to determining the solution sought.
We can define the distance from a point P to a α as the smallest of the distances from the point P up to the infinite points of the plane α. To determine this distance we get the straight perpendicular to the plane α from the point P and I get your point of intersection. The distance from P to I will be the minimum distance to the plane α.
One of the basic problems that we learn by studying the systems of representation are those in which there are elements that are perpendicular to other. All the problems of determining distances make use of these concepts.
Let's see how to determine the line perpendicular to a plane in dihedral system working directly on the main system projections.
One of the most important theorems of descriptive geometry is the so-called “Theorem of the three perpendicular”, It establishes a relation between two lines perpendicular when one of them is parallel to a plane of projection.
