Module 3: Introduction

In this module you will complete the following activities:

Understand how orthogonality allows us to create unique distances between linear objects (points, lines, planes).
Use orthogonality to determine the distance between points, lines, and planes.
Create and resolve algebraic statements relating the distance between points, lines, or planes.
Practice the covered concepts through some exercises, called "Now You Try".
Complete a quiz on this topic at the end of the module.

Introduction

In this module, we will use the geometric properties of various algebraic operations in vector spaces to answer the question "How far apart are these two things?'' Specifically, the "things'' under consideration are points, lines, and planes. The essential tools used will be the norm of a vector, the dot and cross products, and an important application of orthogonality.