ABSTRACT
Vectors and coordinate systems garner less prominence and attention, and are often regarded as mere background features of the CAD environment, or as structures best subsumed into an elegant user interface. While vectors are implicitly employed for any number of modeling tasks, they rarely make an appearance on the screen. The numeric representation of a vector in Cartesian space consists of three numbers that together describe a direction and magnitude. The utility of the dot product is especially evident in the context of projections, from the projection of a point onto a vector to finding the nearest point to a given line, plane, curve or surface. In contrast to the dot product of two vectors, which results in a scalar, the cross product of two vectors results in a vector. The cross product of any two vectors that are not parallel will result in a vector perpendicular to both.
