RECAP: 55mi/hr is NOT a vector, while 55mi/hr West IS a vector.

It's a pretty simple difference, and it will allow us to do many things.

Imagine you take a walk from your home and go three blocks East, then three blocks North.
Where do you wind up?
I bet you have solved questions like this many times.  Just as a review, you know that since West and North are at right angles (90°) and that both parts of the trip are equal in magnitude (3 blocks each), that the resulting final position is at 45° between North and East. How far are you from your start point?  Hopefully you will remember the pythagorean theorem that will give us the length for the 3rd side of any right angle triangle... a² + b² = c² where "c" is the longest side... so for us, 3² + 3² = c², c=4.2blocks. A more proper answer is, "Displacement is 4.2 blocks at an angle of 45° East of North" (or North of East).

Here's another example... Two people push on a cart simultaneously.  They push with equal force AND push in opposite directions. What happens? You should realize that nothing happens!

These examples show an important concept... vectors can be added together.
Police use vectors at crash scenes, pilots use vectors to steer, hunters use vectors to get their trophies... gravity will pull my arrow down so I will aim up; the breeze will push my arrow left so I will aim to the right...
there are loads of examples, so hopefully you can think of some on your own.
Login to Lecture OnLine find the problem called, "5 vectors".
Here is an easy to use program that can show you how to find the components of a vector.  Click at the origin and drag outward... this makes one vector "A"...do it again somewhere new to make vector "B"... now if you hit the "A+B" button, the program adds the vectors together for you to make vector "C"!  The program will do more so you can fool around with it if you want.