Vector–Line–Intersection Construction with 3D/Prism Context

This example demonstrates how to construct a structured geometric diagram in both 2D/3D space by combining vectors, lines, and intersection points, and by using text annotations to clarify the relationships. The key mathematical concepts are vectors (directional geometric representation), lines and their intersections (geometric constraints), and an extended 3D context that may involve solid-like elements such as cylinder/prism settings. Construction highlights: GeoGebra commands are used to build foundational objects step-by-step—Point to create key points (e.g., A_1, B, D_1, D_2, E_1, F, G, H, C), Line to define supporting lines (e.g., i, j, k, l), Vector to display directional vectors (e.g., f, E, m, n, p, q, v, g, u, c), and Intersect to compute intersection points that enforce the geometric constraints (e.g., objects labeled D, E, D_2). Segment is used to connect relevant points for edges or reference geometry, while text1–text4 provide labeling and explanatory marks. Suitable for high school to early undergraduate lessons, especially for visualizing vector ideas alongside geometric constraints and diagram-based modeling.