vinkelrettness

Vinkelrettness is the geometric property of being at a right angle. In Euclidean geometry it describes the relation between two lines, a line and a plane, or two planes that meet to form a 90-degree angle. When two lines lie in a plane, they are perpendicular if they intersect and the angle between them is a right angle. In three-dimensional space, two lines can be perpendicular only if they intersect; otherwise they can be skew, and their directions may be at a right angle without meeting. The concept extends to vectors: two nonzero vectors are perpendicular if their dot product is zero, which means the angle between them is 90 degrees. This notion of orthogonality generalizes to subspaces in linear algebra, and a set of pairwise perpendicular unit vectors forms an orthonormal basis.

The symbol ⟂ is used to denote perpendicularity, for example a ⟂ b and lines l ⟂ m. Perpendicularity is preserved under rigid motions such as translations and rotations, so if two objects are perpendicular, their images under any rigid motion remain perpendicular. Right angles underpin many geometric constructions, and perpendicular lines are central to the definition of the Cartesian coordinate system; axes are perpendicular to each other.

Applications include architecture, engineering, computer graphics, and CAD, where perpendicular relationships simplify measurements, layouts, and computations of distance and projection. In trigonometry, the Pythagorean theorem relates to right angles and perpendicular sides in right triangles.