#AP Pre-Calculus: Vectors - Your Night-Before Review 🚀

Hey! Let's get you super confident about vectors for your AP Pre-Calculus exam. This guide is designed to be quick, clear, and exactly what you need right now. Let's dive in!

#1. Introduction to Vectors

#What are Vectors? 🏹

Vectors are like arrows that have both magnitude (length) and direction. Think of them as representing movement, force, or any quantity with a direction. They're not just numbers; they're like little guided missiles! 🎯

• Tail: Where the vector starts.
• Head: Where the vector ends.

#Visualizing Vectors

Imagine a vector as an arrow on a graph. The arrow's length is its magnitude, and the direction it points is its direction. Simple, right? ↗️

#2. Representing Vectors

#2D Vector Components 🛩️

In a 2D plane, we use components to define a vector. Think of it like giving directions: "move this much in the x-direction, and this much in the y-direction."

• Two Points: Defined by $P1 = (x1, y1)$ (tail) and $P2 = (x2, y2)$ (head).
• Components: $<a, b>$, where $a = x2 - x1$ and $b = y2 - y1$.

#Special Case: The Zero Vector

• $<0, 0>$: When the tail and head are the same point. It has zero magnitude. 🤓

#Trigonometric Components

We can also find vector components using trigonometry. If you know the angle a vector makes with the x-axis and its magnitude, you can find the x and y components using cosine and sine, respectively. 📐