Hoekcomponent

Hoekcomponent is a term used in geometry and vector analysis to denote the component of a vector along a specified direction defined by an angle. The concept is often described in Dutch-language texts as the projection of a vector onto a line that makes a given angle with a reference axis. In English-language literature, the more common term is the projection or the component along a direction, but hoekcomponent can appear in translations or in specialized materials.

Calculation of the hoekcomponent typically involves a vector v and a reference angle θ. If v has Cartesian coordinates (x, y), the hoekcomponent along θ is computed as x cos θ + y sin θ, which is the dot product of v with the unit direction vector (cos θ, sin θ). If the vector is given in polar form as (r, φ), the hoekcomponent along θ is r cos(φ − θ). The orthogonal component to the chosen direction can be obtained as −x sin θ + y cos θ or equivalently r sin(φ − θ).

Extensions to three dimensions replace the angle with a unit direction vector d; the hoekcomponent becomes the scalar projection v · d, equal to |v| cos(angle between v and d). This framework is used in rotating coordinate frames, transforming vectors between reference directions, and simplifying problems in physics, computer graphics, or engineering where directional components are required.

Etymology and usage vary; hoekcomponent is more common in pedagogical or translated material and is not a standard term in all English-language references. Related concepts include vector projection, dot product, and directional decomposition.