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
${\bf w}={\bf u}\times{\bf v}=\left|\begin{array}{lll}
{\bf i} & {\bf j} & {\bf k}\\
2 & 3 & 0\\
-1 & 1 & 0
\end{array}\right|$
$=(0-0){\bf i}-(0-0){\bf j}+(2+3){\bf k}$
$=5{\bf k}$
$|{\bf w}|=\sqrt{0+0+25}=5$
and the unit vector parallel to ${\bf w}$ is
$\displaystyle \frac{{\bf w} }{|{\bf w} |}=\frac{5}{5}{\bf k}={\bf k}$
${\bf w}=5({\bf k})$
${\bf u}\times{\bf v}$ has length $5$ and direction ${\bf k}$
By property 3 (see "Properties of the Cross Product" box on p. 618)
${\bf v}\times{\bf u}=-{\bf w}=5(-{\bf k})$
${\bf v}\times{\bf u}$ has length $5$ and direction $-{\bf k}$
