Answer
${\bf u}\times{\bf v}$ has length $5$ and direction ${\bf k}$
${\bf v}\times{\bf u}$ has length $5$ and direction $-{\bf k}$
Work Step by Step
${\bf u}\times{\bf v}={\bf u}\times{\bf v}=\left|\begin{array}{lll}
{\bf i} & {\bf j} & {\bf k}\\
u_{1} & u_{2} & u_{3}\\
v_{1} & v_{2} & v_{3}
\end{array}\right|$
$=(u_{2}v_{3}-u_{3}v_{2}){\bf i}-(u_{1}v_{3}-u_{3}v_{1}){\bf j}+(u_{1}v_{2}-u_{2}v_{1}){\bf k}$
---
${\bf w}={\bf u}\times{\bf v}=\left|\begin{array}{lll}
{\bf i} & {\bf j} & {\bf k}\\
2 & 3 & 0\\
-1 & 1 & 0
\end{array}\right|$
$=(0-0){\bf i}-(0-0){\bf j}+(2+3){\bf k}$
$=5{\bf k}$
$|{\bf w}|=\sqrt{0+0+25}=5$
and the unit vector parallel to ${\bf w} $is
$\displaystyle \frac{{\bf w} }{|{\bf w} |}=\frac{5}{5}{\bf k}={\bf k}$
${\bf w}=5({\bf k})$
${\bf v}\times{\bf u}=-{\bf w}=5(-{\bf k})$
${\bf u}\times{\bf v}$ has length $5$ and direction ${\bf k}$
${\bf v}\times{\bf u}$ has length $5$ and direction $-{\bf k}$
