vectorfüggvény

A vectorfüggvény, or vector-valued function, is a function whose domain is a set of real numbers and whose codomain is a vector space. More commonly, in calculus, a vectorfüggvény describes a curve or a path in space. The input is typically a single real variable, often representing time or a parameter, and the output is a vector. For example, a vectorfüggvény r(t) might map a scalar value t to a 3D vector (x(t), y(t), z(t)), where x, y, and z are themselves real-valued functions of t.

The components of the vectorfüggvény, x(t), y(t), and z(t), are called scalar component functions. As the parameter t varies, the tip of the vector r(t) traces out a curve in space. This concept is fundamental in physics and engineering for describing motion, trajectories, and fields. Differentiation and integration of vectorfüggvények are analogous to scalar functions. The derivative of a vectorfüggvény r'(t) represents the tangent vector to the curve at a given point, indicating the direction and magnitude of the instantaneous velocity if r(t) describes position over time. The integral of a vectorfüggvény can represent displacement or accumulation of a quantity along a path.