Graphical Representation of Vectors

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.

Examples of vectors

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 \(\text{40}\)\(\text{°}\) 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 \(\text{40}\)\(\text{°}\) angle between the vector and the West direction (the solid arrow below). The direction of this vector can also be described as: W \(\text{40}\)\(\text{°}\) N (West \(\text{40}\)\(\text{°}\) North); or N \(\text{50}\)\(\text{°}\) W (North \(\text{50}\)\(\text{°}\) 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 \(\text{110}\)\(\text{°}\) has been rotated clockwise \(\text{110}\)\(\text{°}\) relative to North. A bearing is always written as a three digit number, for example \(\text{275}\)\(\text{°}\) or \(\text{080}\)\(\text{°}\) (for \(\text{80}\)\(\text{°}\)).