1. Problem: describe vectors and draw some. 2. A vector is a quantity that has both magnitude and direction. 3. A common way to write a vector in 2D is $\vec{v}=\langle a,b\rangle$. 4. Its magnitude is found with the formula $|\vec{v}|=\sqrt{a^2+b^2}$. 5. Important rules: - The order matters: $\langle a,b\rangle$ is different from $\langle b,a\rangle$. - A vector can be shown as an arrow from one point to another. - Vectors with the same length and direction are equal, even if they are in different places. 6. Example vectors: - $\vec{u}=\langle 2,1\rangle$ - $\vec{v}=\langle -1,3\rangle$ - $\vec{w}=\langle 4,-2\rangle$ 7. To draw $\vec{u}=\langle 2,1\rangle$, start at the origin and move 2 units right and 1 unit up. 8. To draw $\vec{v}=\langle -1,3\rangle$, start at the origin and move 1 unit left and 3 units up. 9. To draw $\vec{w}=\langle 4,-2\rangle$, start at the origin and move 4 units right and 2 units down. 10. Final answer: vectors are arrows with direction and size; examples are $\langle 2,1\rangle$, $\langle -1,3\rangle$, and $\langle 4,-2\rangle$.