 Welcome to the wonderful world of vectors. In this video, I'm going to show you some vector basics. I'm going to teach you how you can take a written description of a vector and make a drawing of it and then the opposite. I'll show you how you can take a drawing of a vector and write out the name for that vector. That's called vector notation. The examples I'm going to look at today come out of the handout, Intro to Vectors, which you can find on our Moodle site. Let's get started. Here's a quick example. Let's say you wanted to draw a vector representing displacements of 40 meters left and 80 meters left. Your first vector is just an arrow pointing left that you label with 40 meters. But one thing we want to do with any vector diagram is to draw the vectors to the proper relative magnitude. This means that even though we don't actually draw a vector that is literally 40 meters and another one that's 80 meters long on our paper, we are going to make the diagram of the 80 meter long vector about twice as long as the 40 meter vector. This keeps a nice relative magnitude. Next we will look at vectors that are at an angle. We have two systems for writing out the notations of vectors at angles, the navigational system and the square bracket system. The navigational system works on a weird principle of the English language. Let's check out this awesome photo of teacher band as an example. Now let's say you knew that the drummer in teacher band is Mr. Stridehorst, but you don't actually know what he looks like. So I could tell you that Mr. Stridehorst is right of Mr. Langdale. Now let's think about how we said that. Stridehorst is right of Langdale. So to work out who Stridehorst is, you needed to start off at the end of the sentence and find Langdale first. Then you move to the right to find Stridehorst. This is exactly how the navigational system works. If you needed to draw a 3.0 at 30 degrees north of east vector, you could start off with a little Cartesian plane or an XY axis with the cardinal directions labeled and then you could find 30 degrees north of east by starting at the end of the sentence at east and then drawing out a 30 degree angle starting from east and going to the north in order to get the angle for your vector. This vector is now drawn out at 30 degrees north of east. Here's another example. Let's draw 60 degrees south of west and we won't even worry about the magnitude of the vector for this one. We'll just focus on the direction. We're going to start off on the west axis and then we're going to move south by 60 degrees and draw in our vector and label our angle. This is what 60 degrees south of west looks like. Now let's do the same skill but in reverse. Here's a diagram of a vector. Let's figure out his notation. I can see the angle is drawn in between the east and south axis. To be more specific, the angle is measured from the east moving towards the south. So we say that this is 50 degrees south of east. Note that our vector, 50 degrees south of east is not the same as the vector 50 degrees east of south. These are two totally different angles. However, 50 degrees south of east is equivalent to another angle measurement. We could have measured off the south axis by 40 degrees and gotten the exact same angle. In other words, we could also say that the notation of this vector is 40 degrees east of south. If you're a little confused by this, that is very normal. Every vector has an equivalent vector notation that's called the complementary. And you don't usually need to write out both notations. It's just good to be aware that there's two different ways of doing it when you're getting started. Let's look at a second example. Here we have a 60 degree angle between north and west. The 60 degrees is being measured from north and moves out to the west. So we say that this vector is 60 degrees west of north. Now I don't want to overwhelm you, but I should also mention that the complementary angle to this is 30 degrees north of west. Notice how complementary angles are pretty similar to each other. They always add up to 90 degrees and their notations, the letters are just reverses of one another. The second method of vector addition I'm just going to call the square bracket system. In this system, all angles are measured going counterclockwise from the positive x-axis. And we write the angles with square brackets around them like this. Let's draw out a vector using this notation. 3.0 centimeters, 55 degrees. Again, we're going to start by drawing out a Cartesian plane, but this time we won't put the directions of north, south, east and west on it. Instead, we'll label it at zero degrees here at the positive x-axis. Then 90 degrees, 180 degrees and 270 degrees going counterclockwise. Starting from zero degrees we'll rotate counterclockwise until we've reached approximately 55 degrees and draw our vector. It's actually pretty quick and easy to do angles between zero and 90 degrees with the square bracket system. Here's another example of the square bracket system. We'll draw 120 degrees. We'll begin with the same setup as before labeling the angles in the Cartesian plane. We'll start again at the positive x-axis and then move counterclockwise by 120 degrees. Notice this method works really nicely for angles that are greater than 90 degrees. Now that you have the basics, you can trial this video on adding vectors and breaking them into components.