Let $\mathbf{z}$ be the point one third of the way from $\mathbf{x}$ to $\mathbf{y}$. Using vector arithmetic, express $\mathbf{z}$ in terms of $\mathbf{x}$ and $\mathbf{y}$.
Solution
We are given information of $\mathbf{z}$'s position relative to $\mathbf{x}$ in terms of $\mathbf{y}$'s position relative to $\mathbf{x}$, so we recall