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)

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.

*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

(-3² + 4²) =

(9 + 16) =

(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*:

Shape and Space

Shape and Space

Shape and Space

Shape and Space

Shape and Space

Shape and Space