Combinations of Three Vectors and Plane Construction

This GeoGebra example demonstrates how three vectors u, v, and w can be combined linearly to generate points, segments, and a plane, while auxiliary points A through I form related polygonal structures. It highlights vector addition, scalar multiplication, linear combinations, coplanarity, plane representation, and coordinate relationships in space. The construction uses the Vector command to define vectors and the Plane command to determine a plane from points or vectors, with objects such as A, B, C, D, E, F, G, H, I, u, v, w, a, b, and c linking the geometric configuration. It is suitable for high school vector geometry, introductory linear algebra, or coordinate geometry lessons where students explore how vector combinations determine planes and spatial figures.