Explore the Euclidean dot product in three-dimensional space and its applications in this 28-minute mathematics lecture. Learn about quadrance between points, linear functionals, planes, projections, and Pythagoras' theorem in 3D. Discover how spheres centered at the origin can be represented using quadratic and bilinear equations. Gain insights into perpendicularity and its parallels with two-dimensional concepts. Enhance your understanding of linear algebra and geometry through this comprehensive exploration of circles and spheres using dot products.