perpendicularen

Perpendicularen is a plural term used in geometry to refer to lines, line segments, rays, or planes that meet another geometric object at a right angle (90 degrees). The most common context is perpendicular lines in a plane.

In the plane, a line l has a family of lines that are perpendicular to it. Any line m that is perpendicular to l must intersect l and form a right angle at the point of intersection. All lines perpendicular to a given line are parallel to each other. Through any point P, there is exactly one line perpendicular to l (the line through P that meets l at a right angle). If P lies on l, the perpendicular through P still exists and is unique.

Perpendicularity also applies between a line and a plane. A line is perpendicular to a plane if it intersects the plane at a right angle. A plane can be characterized as perpendicular to a line by containing lines that are all perpendicular to that same line; the line is then a normal to the plane.

In coordinate geometry, perpendicularity is expressed with slopes: if a line has slope m, a line perpendicular to it has slope −1/m (provided the first line is neither vertical nor horizontal). More generally, two nonzero vectors are perpendicular when their dot product is zero. This idea extends to normals of planes: the normal vector is perpendicular to every direction lying in the plane.

Perpendicularen plays a foundational role in constructions, trigonometry, and physics, where right angles define grids, projections, reflections, and normal directions. Related concepts include the perpendicular bisector, orthogonality, and the use of normals in optimization and vector calculus.