Anderson Video - Vector Laws

Professor Anderson
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>> Hello class, Professor Anderson here. Let's talk about some of the vector laws that we need to worry about when we're dealing with these vector problems. Here's a few pretty straightforward ones. First is the commutative law and this just says that A plus B is equal to B plus A. Okay. If I add two vectors graphically, it doesn't matter if I draw A first and then B, I could draw B first and then A, the resultant vector is going to be exactly the same. You could probably also convince yourself rather quickly that the associative law works, which means it doesn't matter what order I add them in. A plus B plus C is equal to A plus B plus C. If I do B plus C first and then add A, it's the exact same as if I did A plus B first and then I added C. And then the one that gives a few people trouble is dealing with subtraction. If I have two vectors, A and B, and I want to subtract the two, how do I visualize that graphically? The way you do it is you're still just adding two vectors. It's just that the second vector you're going to add is the negative of B. The negative of B is exact same length, opposite direction of your original B. The last one that you need to worry about is when you multiply a vector by a scalar. Okay. When I multiply it by a scalar what happens? Well, if I have a vector A that looks like that and I multiply it by a number, say 5, what would 5A look like? It is exact same direction, just five times as long. Okay. That's what a scalar does. Now, let's talk about the components of vectors. This is going to be really important for everything we do in the next few chapters.
>> Hello class, Professor Anderson here. Let's talk about some of the vector laws that we need to worry about when we're dealing with these vector problems. Here's a few pretty straightforward ones. First is the commutative law and this just says that A plus B is equal to B plus A. Okay. If I add two vectors graphically, it doesn't matter if I draw A first and then B, I could draw B first and then A, the resultant vector is going to be exactly the same. You could probably also convince yourself rather quickly that the associative law works, which means it doesn't matter what order I add them in. A plus B plus C is equal to A plus B plus C. If I do B plus C first and then add A, it's the exact same as if I did A plus B first and then I added C. And then the one that gives a few people trouble is dealing with subtraction. If I have two vectors, A and B, and I want to subtract the two, how do I visualize that graphically? The way you do it is you're still just adding two vectors. It's just that the second vector you're going to add is the negative of B. The negative of B is exact same length, opposite direction of your original B. The last one that you need to worry about is when you multiply a vector by a scalar. Okay. When I multiply it by a scalar what happens? Well, if I have a vector A that looks like that and I multiply it by a number, say 5, what would 5A look like? It is exact same direction, just five times as long. Okay. That's what a scalar does. Now, let's talk about the components of vectors. This is going to be really important for everything we do in the next few chapters.