Geometry for Programmers

9 The geometry of vector algebra

This chapter covers

• Definitions and properties of vector products
• Examples of dot, cross, and triple products solving geometric problems in 3D space
• Generalizations of vector products to N-dimensional space where N ≠ 3

Vector algebra is often seen as a staple of applied geometry. Vector products have so much to do with angles, projections, areas, and volumes that it’s hard to imagine doing anything practical without them. Vector algebra is also a never-ending source of interview problems.

In practice, however, vector operations are usually concealed under utility functions’ interfaces to such a degree that about half of candidates who apply for a job in my department can’t tell the dot product from the cross ...