3D Vectors and Prism Geometry: Cosine, Subtraction, and Median (Figure 44)

① This GeoGebra example constructs a three-dimensional prism and demonstrates vector operations, cosine relationships, and median values using its vertices, edges, and faces. ② Core mathematical concepts include 3D vectors, vector subtraction, cosine of the angle between vectors, planes and prism surfaces, midpoints, and geometric mean, along with solid geometry elements such as edges, faces, and diagonals. ③ Construction highlights: the Polygon and Prism commands create the base and solid; Vector defines vectors u, v, w; Plane, OrthogonalLine, and Intersect build auxiliary planes and intersection points; Segment connects key points, Angle measures angles, and Midpoint marks midpoints. Objects include E, F, D, A, B, C, H, G, faces like faceABFE, and edges like edgeAE. ④ Suitable for high school to early college students learning solid geometry and vector algebra, serving as a visual aid for 3D vector operations, cosine theorem applications, and geometric mean demonstrations.