Any vector that is parallel to $\displaystyle \vec{i}+ 2\vec{j}$ is of the form $\displaystyle a\vec{i}+ 2a\vec{j}$. Any vector that is perpendicular to $\displaystyle 3\vec{i}+ \vec{j}$ is of the form $\displaystyle b\vec{i}- 3b\vec{j}$. Find a and b so that $\displaystyle a\vec{i}+ 2a\vec{j}+ b\vec{i}- 3b\vec{j}= \vec{i}+ \vec{j}$