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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.

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Figure 20.1: Examples of vectors

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Figure 20.2: Parts of a vector

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).f6ee959ed70388fff15b5dffa960129a.png

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 ).f9a01c2bce11295d3b9c8342a8540d71.png

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:2791676638581832d993d58764255a0f.png

  • 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.

    =

    Decide on a reference directiond36a8b7028381e67f45f62539e91b613.png

    Determine the length of the arrow at the specific scale.

    If = , then =

    Draw the vector as an arrow.

    Scale used: = 8de51f8849b054eaeb2292bb7e5f1a31.png

    Worked example 2: Drawing vectors 2

    Draw the following vector quantity: east

    Decide on a scale and write it down.

    =

    Decide on a reference directiond36a8b7028381e67f45f62539e91b613.png

    Determine the length of the arrow at the specific scale.

    If = , then =

    Draw the vector as an arrow

    Scale used: =

    Direction = East052f1da002675105035efe2037b75506.png

    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