Stage 29 · Spatial Vectors & Solid Geometry
29.2.5 The Coordinate Formula for the Dot Product
29.2 Putting a Coordinate Grid on Space — The Basis Theorem and Coordinates
Point 5 of 6
29.2.5 The Coordinate Formula for the Dot Product
Core ideaMultiply matching components and add them up — a·b=x₁x₂+y₁y₂+z₁z₂ — with no need to look at a picture anymore.
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.