Lesson 21: Defining Vectors

Just about anything you measure in Physics can be divided into two categories: scalars and vectors.

Scalars: Any measurement that is given as a single number, and nothing else. It has magnitude, but no direction.

Vectors: A measurement that is given as a number and a direction. It has magnitude and direction.

Figure 1
Figure 2

Let’s say you wanted to draw a single vector showing the displacement of an object as it moved from its initial position (d1 )to a final position (d2).

Figure 3

What if there were a bunch of vectors going from d1 to d2?

Vector Directions

We need a system that we can use to give the direction these vectors are pointing in.

Example 1: What is the direction of the vector shown here?

Figure 4

If you look at where the angle is placed in this diagram, you'll probably agree that we are measuring an angle of 30° away from the North.

In fact, the 30° angle is moving towards where East is.

In the physics style of giving a direction, we would write [N30°E], which is read as "North 30° East". The reference line (North) is given first, and then the number of degree away from it (30°) going towards another of the reference lines (East).

We always put directions in [square brackets] to show that they are the direction, and not some weird formula!

Since all the way from North to East is a full 90°, we know that this could also be drawn showing that the vector is 60° (we get it from 90° - 30°) counterclockwise from the East. This would mean that we could also measure this vector as [E60°N] . Of the two [N30°E] is considered more, ummm, polite, since the angle is smaller. Either one is still correct.

There is an older version of this system that still pops up from time to time. In it the order is changed to (1) the number of degrees, (2) towards a reference, (3) from a reference. The example above would be written as [30°E of N] which is read as "30°East of North". We will avoid using this older system.

Try each of the following examples. By clicking on the check mark below and to the right of each you will be able to see if you are correct.