Geometric Construction of Vector Subtraction

This example demonstrates how vector subtraction can be interpreted and constructed geometrically in the plane by converting the difference of two vectors into a corresponding segment/vector. It highlights the underlying phenomenon that a−b is obtained by aligning translated vectors and using directed segments so that the resulting vector matches the subtraction definition. The core concepts include vector arithmetic, the geometric meaning of subtraction, coordinate/coordinate geometry interpretation, and (when connected to lengths) the Pythagorean theorem for understanding relationships among components. Construction-wise, it uses GeoGebra commands such as Vector, Segment, and Point to create the initial vectors and endpoints; Translate to move vectors to the appropriate origin alignment; Rotate to obtain direction-equivalent vectors when needed; If to control conditional logic and switch between constructions; and Show/ShowBoth_1 to reveal or compare key objects. Typical created objects and parameters (e.g., A, B, u, v, u′, v′, TransUV, TransVU, t_1, t_2) form the pipeline from the given vectors to their computed difference. Suitable for high school through first-year university courses, especially for lessons on vectors, analytic geometry, and geometric construction methods.