We think you are located in South Africa. Is this correct?

# Graphical Representation Of Vectors

## 20.2 Graphical representation of vectors

Vectors are drawn as arrows. An arrow has both a magnitude (how long it is) and a direction (the direction in which it points). The starting point of a vector is known as the tail and the end point is known as the head.

### Directions

There are many acceptable methods of writing vectors. As long as the vector has a magnitude and a direction, it is most likely acceptable. These different methods come from the different methods of representing a direction for a vector.

#### Relative directions

The simplest way to show direction is with relative directions: to the left, to the right, forward, backward, up and down.

#### Compass directions

Another common method of expressing directions is to use the points of a compass: North, South, East, and West. If a vector does not point exactly in one of the compass directions, then we use an angle. For example, we can have a vector pointing  North of West. Start with the vector pointing along the West direction (look at the dashed arrow below), then rotate the vector towards the north until there is a  angle between the vector and the West direction (the solid arrow below). The direction of this vector can also be described as: W  N (West  North); or N  W (North  West).  #### Bearing

A further method of expressing direction is to use a bearing. A bearing is a direction relative to a fixed point. Given just an angle, the convention is to define the angle clockwise with respect to North. So, a vector with a direction of  has been rotated clockwise  relative to North. A bearing is always written as a three digit number, for example  or  (for  ). Exercise 20.2See solutions

Classify the following quantities as scalars or vectors:

1.  2.  south

3.  ,  4.  ,  5.  ,  Use two different notations to write down the direction of the vector in each of the following diagrams: • Decide on a reference direction

• Determine the length of the arrow representing the vector, by using the scale.

• Draw the vector as an arrow. Make sure that you fill in the arrow head.

• Fill in the magnitude of the vector.

• # Worked example 1: Drawing vectors 1

Draw the following vector quantity: North

## Decide on a scale and write it down.  =  ## Determine the length of the arrow at the specific scale.

If  =  , then  =  ## Draw the vector as an arrow.

Scale used:  =   # Worked example 2: Drawing vectors 2

Draw the following vector quantity: east

## Decide on a scale and write it down.  =  ## Determine the length of the arrow at the specific scale.

If  =  , then  =  ## Draw the vector as an arrow

Scale used:  =  Exercise 20.3See solutions

Draw each of the following vectors to scale. Indicate the scale that you have used:

1.  south

2.  N  W

3.  ,  East of North

4.  ,  5.  ,  See solutions