1. Let's clarify the problem: You mentioned that the answer is $x - y$ equals the vector $\mathbf{FA}$. We need to understand what $x$, $y$, and $\mathbf{FA}$ represent in this context. 2. Typically, in vector problems, $x$ and $y$ could be vectors or scalar components, and $\mathbf{FA}$ is a vector from point $F$ to point $A$. 3. The formula for a vector between two points $F$ and $A$ is: $$\mathbf{FA} = \mathbf{A} - \mathbf{F}$$ where $\mathbf{A}$ and $\mathbf{F}$ are position vectors of points $A$ and $F$ respectively. 4. If $x$ and $y$ correspond to these position vectors, then: $$x - y = \mathbf{FA}$$ means $x = \mathbf{A}$ and $y = \mathbf{F}$. 5. Therefore, the expression $x - y$ represents the vector from $F$ to $A$, which matches the vector $\mathbf{FA}$. 6. In summary, the problem states that the difference of vectors $x$ and $y$ equals the vector $\mathbf{FA}$, which is consistent with vector subtraction rules. Final answer: $$x - y = \mathbf{FA}$$