# Chapter 8:

### Lines and Planes

## Introduction

In this chapter, you will revisit your knowledge of intersecting lines in two dimensions and extend those ideas into three dimensions. This chapter investigates the nature of planes and intersections of planes and lines, lines with lines, and planes with planes, and helps you develop tools and methods to describe these intersections. For each prescribed section of the chapter, we introduce the general concept and state any vital formulas or definitions. Then, we provide a few basic examples and move on to practice questions to solidify these concepts, and lastly application problems that demonstrate an intuitive understanding of the material. We have provided diagrams where necessary as visual aids.

## 8.1 Equations of lines in Two-Space and Three-Space

## 8.2 Equations of Planes

## 8.3 Properties of planes

## 8.5 Intersection of Lines and Planes

## scenario 1: The line intersects the plane at exactly one point. There is only one solution. | ## scenario 2:The line lies flat on the plane and has infinite points of intersection | ## scenario 3:There is no point of intersection, the line is completely parallel to the surface but is not coincident. |