Geometric Addition and Subtraction of Two Vectors

This example demonstrates the geometric interpretation of adding and subtracting two vectors by constructing vectors head-to-tail (and comparing with subtraction) to reveal how the resulting vector depends on magnitude and direction. It centers on vector addition and subtraction, viewing vectors as directed displacements, and using endpoint relationships to build the corresponding resultant vector. Construction is carried out in GeoGebra using the commands Vector to define vector objects (e.g., aVector, bVector, cVector and related vectors), Point to place vector endpoints and auxiliary points (e.g., A, B, C), Line and Intersect to support any intersection-based auxiliary geometry, and Segment to draw the connecting segments that represent sums/results. The activity is well suited for middle school through early university, particularly for interactive lessons on vectors, direction, and geometric reasoning.