1. **State the problem:** We are given two vectors: $$a = \begin{pmatrix}1 \\ 2\end{pmatrix}, \quad b = \begin{pmatrix}-3 \\ 5\end{pmatrix}$$ We need to: (i) Draw and label vector $2a$. (ii) Draw and label vector $(a - b)$. 2. **Formula and rules:** - To multiply a vector by a scalar, multiply each component by that scalar: $$2a = 2 \times \begin{pmatrix}1 \\ 2\end{pmatrix} = \begin{pmatrix}2 \times 1 \\ 2 \times 2\end{pmatrix} = \begin{pmatrix}2 \\ 4\end{pmatrix}$$ - To subtract vectors, subtract corresponding components: $$a - b = \begin{pmatrix}1 \\ 2\end{pmatrix} - \begin{pmatrix}-3 \\ 5\end{pmatrix} = \begin{pmatrix}1 - (-3) \\ 2 - 5\end{pmatrix} = \begin{pmatrix}4 \\ -3\end{pmatrix}$$ 3. **Intermediate work:** - For $2a$, the vector is $\begin{pmatrix}2 \\ 4\end{pmatrix}$. - For $a - b$, the vector is $\begin{pmatrix}4 \\ -3\end{pmatrix}$. 4. **Explanation:** - Vector $2a$ points to the coordinate $(2,4)$ on the grid. This means starting from the origin $(0,0)$, move 2 units right and 4 units up. - Vector $(a - b)$ points to $(4,-3)$, meaning from the origin move 4 units right and 3 units down. 5. **Final answer:** (i) Vector $2a = \begin{pmatrix}2 \\ 4\end{pmatrix}$. (ii) Vector $a - b = \begin{pmatrix}4 \\ -3\end{pmatrix}$. These vectors can be drawn on their respective grids as instructed.