 Now let's take a look at how I can do vector addition and subtraction using the components of the vectors instead of just using graphical. I want to remind you that the components of the vector are the projections down onto the x and y axis, or we can think of them as the sides of the triangle made up with our vector. Now let's connect this back to what we've seen in graphical vector addition. Real quick, we've got a simulation. I've got two different vectors and it shows their components here. If I wanted to add these two vectors, I would use my tail-to-head method to connect those two vectors up. When I look at the sum of those two vectors, it has components as well. And what I can see is I can move first along the x component and then the y and then the x and then the y, doing my first vector and then my second vector. But I could also take my two x components and add them up and my two y components and add them up. And that's the same triangle that I have for my sum. So my two x's can add and my two y's can add. Now if we take this principle that my vector components add up to give me my result components, I can put this into an equation. So if I've got vector a plus vector b has to give me some result, then I have to start with knowing the components of both vectors, a x, a y, b x, and b y. Then I add the x components. So I take the a x and the b x, those combined together to give me my r x, and I do the same sort of thing for the y, taking my two y components and adding them up. So even if I don't have these vectors graphed out on grid paper, if I know their components, I can add up the components. Similarly with subtraction, I have to start again knowing what those components are, but now I subtract the two x components. So it's a x minus b x. And similarly, a y minus b y to give me my resulting x and y for that subtraction. Let's look at an example. Let's take we have a vector that has a x equals three, a y equals two, and b, which is given by the components one and four for the x and y components. When I add up my x components, that's the three and the one to give me four, and then adding up the y components, which is the two and the four, give me six. And that means my result has an x component of four and a y component of six. If I take those exact same two vectors, but now do subtraction, then I'm taking my three minus my one for the x component and my two minus a four for my y component, giving me a result that has an x component of two and a y component of negative two. Now if I use the i, j, k form of the vectors, which is just a shorthand and again in two dimensions, it's just i and k, the problem becomes even simpler to write down. In the addition case, we can write our a directly above our b with our i's and j's. The two i's add up three plus one to give me four and the two j's add up two plus four to give me six. Subtraction looks very similar, but you have to remember to multiply that negative sign all the way through the equation. So we have three minus one and two minus four to give me my resultant of the subtraction problem. So if you have two vectors and you need to add them or subtract them, component form is a really easy way to do it. We're just adding and subtracting the individual x and y components.