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2D Vector Basics - Example 1

In mathematics, a vector (from the Latin vehere "to transport") is a geometric object that has a magnitude (or length) and a direction. Vectors can be added to other vectors according to vector algebra, and can be multiplied by a scalar (real number). A vector is what is called a "linear" quantity; its magnitude is independent of the chosen basis, and is determined by the component vectors' components. A vector can be pictured as an arrow (or a directed line segment) with a definite magnitude and direction, and having a definite position relative to a chosen origin. The magnitude of the vector is the length of the arrow. The direction of a vector is the direction of the arrow.

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Video Transcript

Okay, so this is gonna be the first example out of R two d vector basics Siri's and it says right each factor in component form. So keep in mind that currently the r and s values that we have are nothing more than just to coordinate points. So if we were to graph it, our would be somewhere around here, so negative three common nine on then s would be right here. Eight common, negative one. But in vectors, remember that the the order does matter with this and that if we have our s, we need to start at our and end at S, which means that the arrow is going this way. So if they had said, s r, then the arrow would go that way. But that's why we have to keep the order consistent with what they have. So because we have it this way, that means we need to find, um, basically the distance between those two coordinate points. And so going from negative 3 to 8, we are adding 11. So it's going to be a positive 11 and then going from, um, going from nine. So for the wise, going from nine to negative one. We are subtracting 10. So then we have negative 10. So our component form of this specter would become 11 Common negative 10. So what if you wanna think about in terms of an equation, you can think of it as the second. So if we have, let's say R s, they are is gonna have a X component and a wife component, and the S is gonna have an X component in the white component. Eso Then we would do X two minus x one. So the x of the s in this case minus the x of the are comma Why of the US minus the y coordinate of the are so again be eight minus negative three, which is how he got the 11 positive 11 because negative minus negative three is going to become positive because two negatives make a positive. And then, for the second component, we've got, um, negative one minus nine, which becomes negative. 10