Answer
${\bf u}\times{\bf v}$ has length $6$ and direction $-{\bf k}$
${\bf v}\times{\bf u}$ has length $6$ and direction ${\bf k}$
Work Step by Step
${\bf w}={\bf u}\times{\bf v}=\left|\begin{array}{lll}
{\bf i} & {\bf j} & {\bf k}\\
2 & 0 & 0\\
0 & -3 & 0
\end{array}\right|$
$=(0-0){\bf i}-(0-0){\bf j}+(-6-0){\bf k}$
$=-6{\bf k}$
$|{\bf w}|=\sqrt{0+0+36}=6$
and the unit vector parallel to ${\bf w}$ is
$\displaystyle \frac{{\bf w} }{|{\bf w} |}=\frac{-6}{6}{\bf k}=-{\bf k}$
${\bf w}=6(-{\bf k})$
${\bf u}\times{\bf v}$ has length $6$ and direction $-{\bf k}$
By property 3 (see "Properties of the Cross Product" box on p. 618)
${\bf v}\times{\bf u}=-{\bf w}=6({\bf k})$
${\bf v}\times{\bf u}$ has length $6$ and direction ${\bf k}$
