Answer
${\bf u}\times{\bf v}$ has length $3$ and direction $\displaystyle \frac{2}{3}{\bf i}+\frac{1}{3}{\bf j}+\frac{2}{3}{\bf k}$
${\bf v}\times{\bf u}$ has length $3$ and direction $-\displaystyle \frac{2}{3}{\bf i}-\frac{1}{3}{\bf j}-\frac{2}{3}{\bf k}$
Work Step by Step
${\bf u}\times{\bf v}={\bf u}\times{\bf v}=\left|\begin{array}{lll}
{\bf i} & {\bf j} & {\bf k}\\
u_{1} & u_{2} & u_{3}\\
v_{1} & v_{2} & v_{3}
\end{array}\right|$
$=(u_{2}v_{3}-u_{3}v_{2}){\bf i}-(u_{1}v_{3}-u_{3}v_{1}){\bf j}+(u_{1}v_{2}-u_{2}v_{1}){\bf k}$
---
${\bf w}={\bf u}\times{\bf v}=\left|\begin{array}{lll}
{\bf i} & {\bf j} & {\bf k}\\
2 & -2 & -1\\
1 & 0 & -1
\end{array}\right|$
$=(2-0){\bf i}-(-2+1){\bf j}+(0+2){\bf k}$
$=2{\bf i}+{\bf j}+2{\bf k}$
$|{\bf w}|=\sqrt{4+1+4}=3$
and the unit vector parallel to ${\bf w} $is
$\displaystyle \frac{{\bf w} }{|{\bf w} |}=\frac{2}{3}{\bf i}+\frac{1}{3}{\bf j}+\frac{2}{3}{\bf k}$
${\bf w}=3(\displaystyle \frac{2}{3}{\bf i}+\frac{1}{3}{\bf j}+\frac{2}{3}{\bf k})$
${\bf v}\displaystyle \times{\bf u}=-{\bf w}=3(-\frac{2}{3}{\bf i}-\frac{1}{3}{\bf j}-\frac{2}{3}{\bf k})$
${\bf u}\times{\bf v}$ has length $3$ and direction $\displaystyle \frac{2}{3}{\bf i}+\frac{1}{3}{\bf j}+\frac{2}{3}{\bf k}$
${\bf v}\times{\bf u}$ has length $3$ and direction $-\displaystyle \frac{2}{3}{\bf i}-\frac{1}{3}{\bf j}-\frac{2}{3}{\bf k}$
