Let $W$ be the set of all vectors of the form $\left[\begin{array}{c} t-3s\cr 3t-3s\cr 5s-3t\cr \end{array}\right]$. Find vectors $\vec{u}$ and $\vec{v}$ in ${\mathbb R}^3$ such that $W=\mathrm{span}\left\lbrace \vec{u}, \vec{v} \right\rbrace$.

$\vec{u}=$ $\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$, $\vec{v}=$ $\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$.