Geometric Simulation of Vector Addition and Subtraction with Angles

This example demonstrates, with an interactive geometric simulation, how vector addition and subtraction are realized in the plane via the head-to-tail composition idea and how the difference vector’s direction and magnitude follow from the construction. It centers on key concepts: vector addition/subtraction, direction angles (e.g., Θ1 and Θ2), and the relationship between vectors and the included angles. The construction uses Intersect to determine crucial endpoints from intersecting geometric entities, Vector to build vectors (such as u, v, w and parameter-driven vectors), Angle to compute/display the relevant angle measures (including α, Θ1, Θ2), and Segment to draw the connecting chains that visually represent the sum/difference. Textfield/Text are used to label parameters and intermediate quantities (e.g., r1, r2, D, a, b, c), while InputBox and buttons support interactive parameter changes. The diagram is suitable for middle to early university levels and works well for instruction, practice, and conceptual exploration of vector composition.