vlakvlak

In geometry, vlakvlak is the Dutch term for a plane: a flat, two-dimensional surface that extends without bound in its own two directions. In three-dimensional Euclidean space, a plane consists of all points that satisfy a linear equation ax + by + cz + d = 0, where (a, b, c) is a normal vector not equal to the zero vector.

A plane can be defined by a point and a nonzero normal vector n, with the condition n · (X − X0) = 0 for any point X on the plane. Equivalently, it can be determined by three non-collinear points. The normal vector is perpendicular to every line contained in the plane.

Key properties: planes have zero thickness and infinite extent. Any two non-parallel planes intersect in a line; parallel planes either do not meet or coincide. The distance from a point P to a plane ax + by + cz + d = 0 is |a xP + b yP + c zP + d| / sqrt(a^2 + b^2 + c^2). The angle between two planes is the angle between their normal vectors, given by cos θ = (n1 · n2) / (|n1||n2|).

Applications include computer graphics, surveying, and geography, where planes model flat surfaces and serve as reference anchors. In higher dimensions the analogue is a hyperplane; the concept generalizes to projective and affine geometries as well.