11. Given $\overrightarrow{A B}=6 \vec{i}+\vec{j}, \overrightarrow{B C}=x \vec{i}+y \vec{j}, \overrightarrow{C D}=-2 \vec{i}-3 \vec{j}$, and $\overrightarrow{B C} / / \overrightarrow{D A}$. Find the relationship between $x$ and $y$.
11. $\overrightarrow{D A}=\overrightarrow{D C}+\overrightarrow{C B}+\overrightarrow{B A}=(-4,-x) \vec{i}+(2-y) \vec{j}$, from $\overrightarrow{B C} / / \overrightarrow{D A}$ we get $(-4-x) \cdot y=$ $(2-y) \cdot x$, which simplifies to $x+2 y=0$.