# Vector notation

**Vectors and scalars**

Vector – this is a quantity that has a size and direction (e.g. displacement, velocity, force)

Scalar – a quantity with a size or magnitude only (e.g. length, speed, mass)

**Representing vectors**

When representing vectors, the **magnitude** is given by the length of the line and the **direction** is given by the arrow on the line.

For example, the vector below is represented as a column vector as follows:

AB – represent the direction

6 – is the horizontal unit of movement

3 – is the vertical unit of movement

**The negative of a vector**

A negative or inverse vector is represented as:

This vector is represented as:

**The zero and unit vector**

A vector with a magnitude of 0 is called the **zero vector **and vector with a magnitude of 1 is called a **unit vector.**

**The unit base vectors**

Column vectors can easily be written in terms of **i** and **j**. For example,

In the example above, the number of **i**’s demonstrates how many units are moved horizontally and the number of **j**’s demonstrates how many units are moved vertically.