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
${\bf u}\times{\bf v}=\left|\begin{array}{lll}
{\bf i} & {\bf j} & {\bf k}\\
u_{1} & u_{2} & u_{3}\\
v_{1} & v_{2} & v_{3}
\end{array}\right|$
$=(u_{2}v_{3}-u_{3}v_{2}){\bf i}-(u_{1}v_{3}-u_{3}v_{1}){\bf j}+(u_{1}v_{2}-u_{2}v_{1}){\bf k}$
---
${\bf w}={\bf u}\times{\bf v}=\left|\begin{array}{lll}
{\bf i} & {\bf j} & {\bf k}\\
-8 & -2 & -4\\
2 & 2 & 1
\end{array}\right|$
$=(-2+8){\bf i}-(-8+8){\bf j}+(-16+4){\bf k}$
$=6{\bf i}-12{\bf k}$
$|{\bf w}|=\sqrt{36+144}=\sqrt{180}=6\sqrt{5}$
and the unit vector parallel to ${\bf w} $is
$\displaystyle \frac{{\bf w} }{|{\bf w} |}= \frac{6}{6\sqrt{5}}{\bf i}-\frac{12}{6\sqrt{5}}{\bf k}$
${\bf w}=6\displaystyle \sqrt{5}( \frac{\sqrt{5}}{5}{\bf i}-\frac{2\sqrt{5}}{5}{\bf k})$
${\bf v}\displaystyle \times{\bf u}=-{\bf w}=6\sqrt{5}( -\frac{\sqrt{5}}{5}{\bf i}+\frac{2\sqrt{5}}{5}{\bf k})$
${\bf u}\times{\bf v}$ has length $6\sqrt{5}$ and direction$ \displaystyle \frac{\sqrt{5}}{5}{\bf i}-\frac{2\sqrt{5}}{5}{\bf k}$
${\bf v}\times{\bf u}$ has length $6\sqrt{5}$ and direction $ -\displaystyle \frac{\sqrt{5}}{5}{\bf i}\frac{2\sqrt{5}}{5}{\bf k}$
