Answer
${\bf u}\times{\bf v}$ has length $6\sqrt{5}$ and direction $\displaystyle \frac{\sqrt{5}}{5}{\bf i}-\frac{2\sqrt{5}}{5}{\bf k}$
${\bf v}\times{\bf u}$ has length $6\sqrt{5}$ and direction $-\displaystyle \frac{\sqrt{5}}{5}{\bf i}+\frac{2\sqrt{5}}{5}{\bf k}$
Work Step by Step
${\bf w}={\bf u}\times{\bf v}=\left|\begin{array}{lll}
{\bf i} & {\bf j} & {\bf k}\\
-8 & -2 & -4\\
2 & 2 & 1
\end{array}\right|$
$=(-2+8){\bf i}-(-8+8){\bf j}+(-16+4){\bf k}$
$=6{\bf i}-12{\bf k}$
$|{\bf w}|=\sqrt{36+144}=\sqrt{180}=6\sqrt{5}$
and the unit vector parallel to ${\bf w}$ is
$\displaystyle \frac{{\bf w} }{|{\bf w} |}= \frac{6}{6\sqrt{5}}{\bf i}-\frac{12}{6\sqrt{5}}{\bf k}$
${\bf w}=6\displaystyle \sqrt{5}( \frac{\sqrt{5}}{5}{\bf i}-\frac{2\sqrt{5}}{5}{\bf k})$
${\bf u}\times{\bf v}$ has length $6\sqrt{5}$ and direction $\displaystyle \frac{\sqrt{5}}{5}{\bf i}-\frac{2\sqrt{5}}{5}{\bf k}$
By property 3 (see "Properties of the Cross Product" box on p. 618)
${\bf v}\displaystyle \times{\bf u}=-{\bf w}=6\sqrt{5}( -\frac{\sqrt{5}}{5}{\bf i}+\frac{2\sqrt{5}}{5}{\bf k})$
${\bf v}\times{\bf u}$ has length $6\sqrt{5}$ and direction $-\displaystyle \frac{\sqrt{5}}{5}{\bf i}+\frac{2\sqrt{5}}{5}{\bf k}$
