Stage 29 · Spatial Vectors & Solid Geometry

29.2.6 Formulas for Length, Distance, and Angle

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

Point 6 of 6

29.2.6 Formulas for Length, Distance, and Angle

Core idea

The square root of the summed squared coordinate differences is the distance between two points, and cosθ falls straight out of the coordinates too.

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 · 29.2.6 Formulas for Length, Distance, and Angle