 So we've discussed the fact that lots of physical quantities have magnitude and direction. For example, displacement, velocity, acceleration, and Adele talked about forces. So all these different things that have a magnitude and a direction, and they're called vectors. And they can be quite tricky to deal with because they're going in different directions. If you want to add them together, then you need to do all sorts of trigonometry. Vanessa showed us a really cool way of dealing with that by breaking them down into components. For example, north and east, or if you had three dimensions, you might need north, east, and up, down. And we're going to look more closely now at vector notation in order to see how to deal with this in algebraic form. So what we're talking about here is that vector equations have all sorts of rules, just like normal equations do. Let's look at one of the first vector equations we've seen. We've seen the definition of velocity. So velocity, which is a vector, is equal to the change in position over a change in time. Now that looks like just a number equals a number divided by another number. But we know that both velocity and position, these two things, have a direction. And so we needed to get the direction right. When we were doing all of this in one dimension, just along a line, we didn't worry about the direction. But when we do have to worry about the direction, then we need to realize that the velocity is a vector. We just put the arrow on it to say that it's got a direction. And this change in position is also a vector, so it's got to have an arrow on it. So this is a vector equation.