Vector Ratio Theorem: Dividing Vectors via Parallelogram Construction

This example demonstrates the vector ratio (dividing) theorem geometrically: given two vectors with compatible directions, it constructs a parallelogram-style figure and locates points on the sides using a proportional split, so the resulting segments correspond to “division” of vectors (ratio relationships). Key concepts include vectors, parallelogram geometry as a vector representation, and the use of distances/lengths to encode proportionality. The construction uses GeoGebra commands and objects such as Vector and Point to create vector endpoints, Segment to build the sides, Distance/Length to compute required metrics, and Semicircle plus PointIn to enforce or visualize allowed regions/constraints. Conditional logic via If selects constructions based on validity, while Max helps manage extremal/feasible values. Objects like mid, m, n, AB, and M serve for intermediate points and labels, and text1–text3 with button1 support parameter display and interactive results. Suitable for advanced high school and early university students learning vectors and geometric modeling, and for classroom demonstrations linking ratios and vector operations.