Definition: A directed quantity, one with both magnitude and direction; the signed difference between two points.

Alright class, settle down, let’s take a look, At a word that’s important, a geometric hook! We’re talking about a vector , it's true, And understanding this will help you see things through. The dictionary gives us a helpful plea, “A directed quantity… for you and me!” It says it has both a size and a way, To point its direction, day after day. Think of it like this, a journey's bright start, From one place to another, playing a part. We need to know how far , that’s the magnitude you see, The length of the path, for all to agree! And then we have the direction , don't you know? Like North or South, where the breezes flow. It tells us which way the journey will go, A line that’s pointing, steady and slow. The "signed difference between two points" – That's how we define it, with scientific joints! Imagine a starting spot, then a place you’ve reached, A vector shows the distance, carefully beseeched. So remember this lesson, bright and bold, A vector’s got magnitude, a story to be told. It's about size and direction too, Now go forth and apply it, just for you! Do you have any questions? Let's discuss!