Adding Integers: Geometric Demonstration with Vectors and Planes in 3D

Construct a 3D coordinate-space geometric setup to visually represent integer-like addition using vectors and connecting segments. Create a vertical reference segment that provides two endpoints, then define vector u as the displacement from a fixed left vertical position to the corresponding point at the same y-level (with the same x shift). Define vector v at a second y-reference level as the displacement from a vertical-offset point to a point shifted by b in the horizontal direction. Next draw segment c connecting an existing point to the endpoint of vector v, and draw segment d connecting the start point of vector u to the start point of vector v. Include an additional short vertical segment e on the same left reference axis as a base reference, then present the relationships between these vectors and segments.