Stage 29 · Spatial Vectors & Solid Geometry

29.2.1 The Basis Theorem for Spatial Vectors

29.2 Putting a Coordinate Grid on Space — The Basis Theorem and Coordinates

Point 1 of 6

29.2.1 The Basis Theorem for Spatial Vectors

Core idea

Pick three non-coplanar arrows as a basis, and any vector at all can be assembled as xa+yb+zc.

Module goal. Use three non-coplanar vectors as a "skeleton" to describe every vector in space, then set up a 3D coordinate system that turns both vectors and points into three numbers, laying the groundwork for the calculations ahead.

eastmath.com · 29.2 Putting a Coordinate Grid on Space — The Basis Theorem and Coordinates · 29.2.1 The Basis Theorem for Spatial Vectors