Vector Basics

Introduction

A vectors have magnitude and direction, and there are many ways to represent them. In this Learn page we will start by investigating the ways of representing vectors, and then go on to defining planes and lines in vector forms, and working out angles between vectors etc.

Component form

In two dimensions vectors are often represented as arrows. We can represent this vector as the distance from the origin of it’s end point in each of the two directions (when we have two dimensions):


These distances are given in terms of the unit vectors (These are vectors of length 1 in only 1 direction (x,y,z)). This distinguishes the vector from a simple co-ordinates.

The unit vectors tend to be called the following:

  • i in the x direction
  • j in the y direction
  • k in the z direction

This therefore extends to three dimensions and beyond nicely. So how is this written? Well say, for example, the vector is 3 in the x direction and 5 in the y direction, the vector will be written out as (in component form):