Answer
$\vec{x}-\vec{y}$ is perpendicular to $\vec{p}$
Work Step by Step
$\vec{p}-\vec{x}=\vec{k}$ and $\vec{p}-\vec{y}=\vec{k}$
Now, $\vec{p}(\vec{x}-\vec{y})=\vec {p} \vec{x}-\vec{p} \vec{y} \\=k-k\\=0 $
This implies that $\vec{x}-\vec{y}$ is perpendicular to $\vec{p}$.
