### Introduction

Vectors are very convenient tools for analysing lines and planes in three dimensions. In this Section you will learn about direction ratios and direction cosines and then how to formulate the vector equation of a line and the vector equation of a plane. Direction ratios provide a convenient way of specifying the direction of a line in three dimensional space. Direction cosines are the cosines of the angles between a line and the coordinate axes. We begin this Section by showing how these quantities are calculated.

#### Prerequisites

- understand and be able to calculate the scalar product of two vectors
- understand and be able to calculate the vector product of two vectors

#### Learning Outcomes

- obtain the vector equation of a line
- obtain the vector equation of a plane passing through a given point and which is perpendicular to a given vector
- obtain the vector equation of a plane which is a given distance from the origin and which is perpendicular to a given vector

#### Contents

1 The direction ratio and direction cosines2 Direction ratios and cosines in three dimensions

3 The vector equation of a line

3.1 Cartesian form

4 The vector equation of a plane