In order to describe a vector, we use two quantities, its magnitude and direction.

Magnitude

The magnitude of a vector is simply the number that describes how big (or small) the vector is.  The number can be any positive number or zero.  It can be a fraction or decimal number to any precision that you can measure.  For example, a ruler has a length of 1.00 m.  If the ruler were a vector, its length is its magnitude.

Direction

The direction is the way the vector points.  This is what makes the vector very different from a number.  If you want to make a measurement using the ruler, you need to point it in the proper direction.

For example, a table could have a length of 2.0 meters, a width of 2.5 meters, and a height of 0.8 m.  These sizes point in different directions.

A short table

If we changed the direction of them, we could end up with a very different table.

A tall table

From this you can see that the directions of the vectors are important.  When you describe a vector, you should give both its magnitude and direction.

When solving problems in physics, it is helpful to define a convenient coordinate system.  We report the direction of a vector relative to one of the coordinate axes.  Many of our introductory physics problems will use a simple x-y coordinate system.  In this case, we would usually measure the direction as an angle from the x-axis.

The next thing to note about vectors is that they don’t add like numbers.  If we added up 2.5 m, 1.5 m, and 0.8 m, we would end up with 4.8 m.  However, this addition doesn’t make sense in our example of the table.  We would keep each of the measurements separate, because the directions matter.

There are ways to combine vectors that do make sense.  We’ll look at these in a later lesson.