Vector Functions in 3D: Parameterized Curves via Vectors

This example demonstrates how to construct vector functions in three-dimensional space using a parameterized (Cartesian) description, linking the evolution of vectors to a space curve and to related quantity ideas such as proportions and definite integrals. It focuses on key concepts including 3D vectors (magnitude and direction), vector-valued functions, and parametric curve visualization in 3D (graphing in space). Construction-wise, the GeoGebra setup uses CurveCartesian to build the Cartesian space curve C from the component functions f, g, h, and uses Vector to create vector objects tied to the parameter t (with an initial parameter t0). Additional objects r and A serve as parameters for scaling, direction, or initial placement of vectors. Suitable for high school to early university, especially for calculus/analytic geometry instruction and interactive exploration of vector-function geometry.