Vector algebra and analytic geometry of space form the bridge between algebra and geometry. Vectors give a compact language for describing direction and magnitude, while analytic geometry turns points, lines, planes, and curved surfaces into equations you can manipulate.

What You Will Learn

• Historical Background — how vectors were invented, told through a simple real-world scenario.
• Basic Concepts and Operations — vector definition, linear operations, coordinate representation, and linear combinations.
• Products of Vectors — the dot product, cross product, and scalar triple product, with their geometric meaning.
• Analytic Geometry of Space — coordinates, equations of lines and planes, positional relationships, and distance/angle formulas.
• Quadric Surfaces — spheres, ellipsoids, paraboloids, hyperboloids, and cones.

Suggested Order

Prerequisites: basic functions and coordinate geometry. Start with the Historical Background for intuition, then work through the modules in order.