Consider quadrilateral $ABCD$ and point $P$ on the same plane. Let $\vec{AB}=\vec{a}, \vec{BC}=\vec{b}$ and $\vec{CD}=\vec{c}$.
If $\vec{PA}+\vec{PB}+\vec{PC}+\vec{PD}=\vec{AD}$, find $\vec{AP}$ in terms of $\vec{a}, \vec{b}$ and $\vec{c}$.

$\vec{AP}=$ Check

Consider parallelogram $ABCD$. Let the midpoint of $BC$ and $CD$ be $E$ and $F$ respectively.
If $\vec{AE}=\vec{u}$ and $\vec{AF}=\vec{v}$, find $\vec{AB}$ and $\vec{AD}$ in terms of $\vec{u}$ and $\vec{v}$.

$\vec{AB}=$ Check
$\vec{AD}=$ Check

Let $\vec{a}=\binom{-3}{2}$ and $\vec{b}=\binom{2}{1}$.
Find the value of $t$ that gives the minimum value of $\left \vert \vec{a}+t\vec{b} \right \vert$.

$t=$ Check
minimum value of $\left \vert \vec{a}+t\vec{b} \right \vert =$ Check