1. **Problem:** Describe vectors and draw some to understand how they work. 2. A **vector** is a quantity that has **magnitude** and **direction**. - The magnitude tells how long the vector is. - The direction tells which way it points. 3. A vector is often written as $\langle a, b \rangle$ in two dimensions. - $a$ is the horizontal change. - $b$ is the vertical change. - For example, $\langle 3, 2 \rangle$ means move 3 units right and 2 units up. 4. A vector can also be shown as an arrow from one point to another. - The tail is where the arrow starts. - The head is where the arrow ends. - The arrow length represents magnitude. 5. Important rules: - Vectors can be moved anywhere without changing them, as long as direction and length stay the same. - Two vectors are equal if they have the same magnitude and direction. - The zero vector is $\langle 0, 0 \rangle$, which has no length and no direction. 6. Examples of vectors: - $\langle 2, 1 \rangle$: 2 right, 1 up. - $\langle -3, 2 \rangle$: 3 left, 2 up. - $\langle 1, -4 \rangle$: 1 right, 4 down. 7. A simple way to visualize them: - If you start at the origin $(0,0)$ and end at $(3,2)$, the vector is $\langle 3,2 \rangle$. - If you start at the origin and end at $(-3,2)$, the vector is $\langle -3,2 \rangle$. - If you start at the origin and end at $(1,-4)$, the vector is $\langle 1,-4 \rangle$. 8. Final idea: vectors are arrows that show both **how far** and **which way**. **Answer:** Vectors are quantities with magnitude and direction, and they are often drawn as arrows such as $\langle 3,2 \rangle$, $\langle -3,2 \rangle$, and $\langle 1,-4 \rangle$ to show movement in different directions.