Mathematics

The key is remembering that a displacement vector between two points is found by subtracting position vectors: the vector from $P$ to $Q$ equals $\mathbf{q} - \mathbf{p}$. Once you identify which position vector belongs to each point and subtract in the right order, the algebra becomes straightforward—just combine like terms in $\mathbf{a}$ and $\mathbf{b}$.

The key is remembering that a displacement vector between two points is found by subtracting position vectors: the vector from $P$ to $Q$ equals $\mathbf{q} - \mathbf{p}$. Once you identify which position vector belongs to each point and subtract in the right order, the algebra becomes straightforward—just combine like terms in $\mathbf{a}$ and $\mathbf{b}$.