One of the most important topics taught at the start of introductory physics is the idea of vectors. Students really need proficiency with them if they are to use force and momentum.

Just about every course covers this, of course, but I will do it a little differently. I’ll use python to help students hone their vector skills. But first, a quick intro to the subject.

Here is a definition I’m not fond of:

It’s not wrong, but I don’t like emphasizing direction. It seems to indicate that you can express a vector with only a number and an angle. (Yes, I know it doesn’t actually say that, but that’s what some students read into it.) OK, here is my definition, which I admit is not perfect:

But how do you use a vector? I won’t go over this in detail, as I’ve done so before. How about the highlights?

One way of representing a vector is to list its x,y, and z components. Something like v = <1,2,3> m/s. Of course there are many ways to represent a vector.

There is a thing called vector addition. If

**A**and**B**are vectors, then**A**+**B**=**C**, where**C**also is a vector. The components of vector**C**are the sum of the components of**A**and**B**. (People typically distinguish vector variables from scalars by drawing an arrow over it, but that’s not easy to do when typing so I used boldface.)Scalar multiplication is when a vector is multiplied by a scalar. To find the result, you merely multiply each vector component by the scalar value.

The magnitude of a vector is the square root of the sum of the squares of the components. Yes, that’s terrible to write out but I’m just trying to move on.

A unit vector is a vector with a magnitude of one and no units—yes, that seems weird. The main idea of a unit vector is to describe the direction of a vector. Trust me, it’s useful.