Track triangle (vector calculation)

Track triangle in vector geometry
(sketch)

As track triangle of a plane in three-dimensional space is referred to in the analytical geometry that of triangle that of the trace line , that is from the line of intersection of this plane with the three coordinate planes is limited. The line of intersection of two non- coplanar planes is defined as the set of all points that lie in both planes at the same time. The corners of the track triangle lie on the coordinate axes and are therefore the track points of the plane under consideration. The track triangle only exists if the given plane is not parallel to any of the coordinate planes.

If the track triangle is known, the axis intercept form of the plane equation can be specified immediately . Are , and the corners of the track triangle (with , , ), this is the intercept of the form ${\displaystyle (a|0|0)}$ ${\displaystyle (0|b|0)}$ ${\displaystyle (0|0|c)}$ ${\displaystyle a\neq 0}$ ${\displaystyle b\neq 0}$ ${\displaystyle c\neq 0}$

${\displaystyle {\frac {x}{a}}+{\frac {y}{b}}+{\frac {z}{c}}=1}$.

There is a computational and a graphical solution for determining the axis intercepts and thus the track triangle from a plane given in normal form or parameter form (position vector and two direction vectors).