1. **Problem Statement:** We are given a point $P$ with position vector $$\begin{pmatrix} 3 \\ -17 \end{pmatrix}$$ We need to write the vectors: a) $\overrightarrow{OP}$ b) $\overrightarrow{PO}$ as column vectors. 2. **Understanding the vectors:** - $\overrightarrow{OP}$ is the vector from the origin $O$ to the point $P$. This is exactly the position vector of $P$. - $\overrightarrow{PO}$ is the vector from point $P$ back to the origin $O$. This is the negative of $\overrightarrow{OP}$. 3. **Writing $\overrightarrow{OP}$:** Since $P$ has position vector $$\begin{pmatrix} 3 \\ -17 \end{pmatrix},$$ we have $$\overrightarrow{OP} = \begin{pmatrix} 3 \\ -17 \end{pmatrix}.$$ 4. **Writing $\overrightarrow{PO}$:** This vector points from $P$ to $O$, so it is the negative of $\overrightarrow{OP}$: $$\overrightarrow{PO} = -\overrightarrow{OP} = -\begin{pmatrix} 3 \\ -17 \end{pmatrix} = \begin{pmatrix} -3 \\ 17 \end{pmatrix}.$$ **Final answers:** - a) $\overrightarrow{OP} = \begin{pmatrix} 3 \\ -17 \end{pmatrix}$ - b) $\overrightarrow{PO} = \begin{pmatrix} -3 \\ 17 \end{pmatrix}$