 So now I want to give you a brief introduction to some of the notation associated with vectors. Again, a vector is a physical quantity that has both a magnitude and a direction. We're describing how much and which way. An arrow, again, is one of our most common ways we represent that vector, where the length of the arrow represents the magnitude and the direction is shown by which way the arrow is pointing. Now in terms of our position coordinates, this is kind of like the r and the theta. How far you are from the origin and what angle you are at around. When I have an arrow representing the vector, it starts at the tail and points towards the head. So the head is the pointed end of the vector arrow, and the tail is the base of it. If I'm going to write these physical quantities as symbols, then I'm going to want to represent the difference between vectors and scalars. Now before I start here, I'm going to use a generic vector A. But that could be anything. We're going to use the same sort of notation all the way through. So if I have a vector A, you're often going to see it in textbooks as a bold font. And that bold font represents the fact that it's a vector. If that same A was just a scalar, it would be printed out in a normal font. Now sometimes it's hard to tell the difference between a normal font and a bold font, especially if you're doing things written by hand. So we need something a little bit clearer sometimes. And so if you've got a vector, you're going to want to have that arrow on top. So if you have one quantity that's written with an arrow on the top, you know that quantity is a vector. If it's in just a normal font without the arrow on top, it's probably a scalar. If you want to make sure that it's absolutely clear that you're talking just about how much, we can use the absolute value signs. And the absolute value signs means I'm talking about the magnitude or how much of quantity A I have without any regard to the direction. So when you see the arrow on top, you know it's a vector. If you see the absolute value signs, you know it's a scalar. Let's talk about components. If I've got this vector shown as an arrow, how do I describe that mathematically? Well, one of the methods we can use is components, which is the projection of that arrow along the x and y-axis, like this. In this case, if the black represents my vector a, my present projection of that down onto the x-axis, what's shown here in red, is the x-component of vector a. And the projection here along the y-axis is the y-component of vector a. So we use these subscripts x and y to say that I'm not talking about the entire vector. I'm only talking about the components in certain directions. Now having it shown here along the axes is one way we can show the components, but it's not the only way. I can also move that a sub y vector over, same length, but now I'm representing it as a triangle. So now the vector a is the hypotenuse of the triangle, and the a sub x and a sub y, the components, form the sides of the triangle. So it's the same concept either way, but it's just kind of shown to you in a little bit of a different way. Now another way that you're going to see, and we're going to have to explain this in more detail, is the i, j, k notation. And this is really just sort of a compact representation of a vector. If I've got this vector a, and I've got the components a, x, and a, y, it might be convenient to be able to represent them in an equation to be able to do the math a little bit easier. And that's really what this i, j, k notation is about. So for example, if a, x was 3 and a, y was 5, when I put that together, I could represent this vector more compactly as the vector a is 3i hat plus 5j hat, or the x part, which always goes with i, is 3. And the y part, which always goes with j, is 5. If you happen to have a 3D vector, such as you've got a z component, you'd have an extra term out here which have a k. Again, these vector notations is just a brief overview to give you an idea of what we're talking about before we get into actually dealing with the math of our vectors in physics.