For most of the problems we will be
facing in the next few weeks, we will only
need to work in two dimensions.
We use a 2D coordinate system so we can formally put vectors
on a grid and more easily do these vector operations.
Once we have our axes, the next thing we need are unit vectors.
Unit vectors have a magnitude of 1
and are in a defined direction.
For a normal x, y coordinate system,
we have i hat in the positive x direction and j hat
in the positive y direction.
In Cartesian coordinates, the unit vectors
are the same no matter what point in space we're at.
We can also define a unit vector in the direction
of an arbitrary vector.
The key here is to make sure it has a magnitude of 1.