1. **Stating the problem:** We are given that $\overrightarrow{AB} = \mathbf{p}$. We need to express: a) $\overrightarrow{CD}$ in terms of $\mathbf{p}$. b) $\overrightarrow{DC}$ in terms of $\mathbf{p}$. 2. **Understanding vector notation:** - $\overrightarrow{AB}$ is the vector from point A to point B. - $\overrightarrow{CD}$ is the vector from point C to point D. - $\overrightarrow{DC}$ is the vector from point D to point C. 3. **Key vector properties:** - The vector from one point to another is the negative of the vector in the opposite direction: $$\overrightarrow{DC} = -\overrightarrow{CD}$$ - If $\overrightarrow{CD}$ is equal to $\overrightarrow{AB}$, then $\overrightarrow{CD} = \mathbf{p}$. 4. **Expressing $\overrightarrow{CD}$ in terms of $\mathbf{p}$:** Since the problem's diagram and description imply $\overrightarrow{CD}$ is the same vector as $\overrightarrow{AB}$, we have: $$\overrightarrow{CD} = \mathbf{p}$$ 5. **Expressing $\overrightarrow{DC}$ in terms of $\mathbf{p}$:** Using the property that reversing the direction negates the vector: $$\overrightarrow{DC} = -\overrightarrow{CD} = -\mathbf{p}$$ **Final answers:** - a) $\overrightarrow{CD} = \mathbf{p}$ - b) $\overrightarrow{DC} = -\mathbf{p}$