A vector $a$ starts at $P_1$ and ends at $P_2$ . Express the vector $a$ in terms of $i$ and $j$.

$P_1=(-3,4)$, $P_2=(5,-2)$

A vector $a$ starts at $P_1$ and ends at $P_2$. Express the vector $a$ in terms of $i$ and $j$.

$P_1=(-31,44)$, $P_2=(35,-28)$

A vector $u$ has a magnitude of $20$ and makes an angle of ${315}^{\circ }$ with the positive $x$-axis. Write the vector $u$ in terms of $i$ and $j$.