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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. south

2. ,

3. ,

4. ,

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

=

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

=

Determine the length of the arrow at the specific scale.

If = , then =

Draw the vector as an arrow

Scale used: =

Direction = East

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