# Vectors

Source: https://projectgcse.co.uk/maths/shape_space/vectors

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A vector quantity has both length (magnitude) and direction. The opposite is a scalar quantity, which only has magnitude. Vectors can be denoted by **AB**, **a**, or _AB_ (with an arrow above the letters).
If **a** = (3) then the vector will look as follows:
(2)

![](https://content.projectgcse.co.uk/img/maths/vector.gif)

NB1: When writing vectors as one number above another in brackets, this is known as a column vector.
NB2: in textbooks and here, vectors are indicated by bold type. However, when you write them, you need to put a line underneath the vector to indicate it.

![](https://content.projectgcse.co.uk/img/maths/vector23.gif)

_Example_:
If **a** = (-5) and **b** = ( 2), find the magnitude of their resultant.
( 3)(1)

The resultant of two or more vectors is their sum.
The resultant therefore is (-3).
( 4)
The magnitude of this is

![](https://content.projectgcse.co.uk/img/maths/root.gif)

(-3² + 4²) =

![](https://www.projectgcse.co.uk/pics/root.gif)

(9 + 16) =

![](https://content.projectgcse.co.uk/img/maths/root.gif)

(25) = 5

The addition and subtraction of vectors can be shown diagrammatically. To find **a** + **b**, draw **a** and then draw **b** at the end of **a**. The resultant is the line between the start of **a** and the end of **b**.
To find **a** - **b**, find -**b** (see above) and add this to **a**.

_Example_:

![](https://content.projectgcse.co.uk/img/maths/vectors.gif)