Scalar Triple Product to Build the Volume of a Parallelepiped

This example demonstrates how the scalar triple product of three vectors determines the volume of a parallelepiped, using shifting/offset vectors to reveal the geometric meaning behind the computed volume. It centers on key ideas such as vector dot and cross products, the definition and interpretation of the scalar triple product, the role of a normal (perpendicular) direction in expressing volume as base area times height, and the construction of a 3D parallelepiped from its generating vectors. Construction-wise, the diagram is assembled from polygons (Polygon) using points like P, S, Q, O, A, B, C, D to form the faces, while vector objects (Vector) such as q, a, s, o, b, c, d encode the directions and shifts that position the vertices consistently. The resulting solid gives an intuitive bridge between vector algebra and solid geometry. Suitable for high school enrichment and early undergraduate linear algebra/solid geometry lessons, as well as self-study and interactive classroom demonstrations.