Vertikalplan

Vertikalplan, or vertical plane, is a geometric concept used in mathematics, surveying, architecture and civil engineering to describe a plane that is oriented vertically with respect to a reference horizontal plane. In a standard three-dimensional coordinate system where the horizontal plane is z = 0, a vertical plane is typically given by an equation of the form ax + by = c, which does not involve z. This means the plane extends indefinitely in the vertical direction and in one horizontal direction, and its intersection with the horizontal plane is a straight line.

Key properties include that a vertical plane contains all vertical lines (lines parallel to the vertical axis) and is perpendicular to the horizontal plane. Its intersection with the horizontal plane is a single line, and the plane can be moved or rotated around that line to describe different vertical surfaces.

In practical applications, vertical planes are used to model walls, facades, and other surfaces that are oriented upright. In surveying and cartography, they help define vertical cross-sections or profiles of terrain and objects. In architecture and building design, they aid in analyzing elevations and structural alignment. The concept contrasts with horizontal planes (perpendicular to the vertical direction) and with oblique planes, which are not strictly vertical or horizontal.

See also: plane, vertical cross-section, projection, cross-section, horizontal plane.