Answer
$a.\quad 1$
$b.\quad 1$
Work Step by Step
$ a.\quad$
The area of the paralellogram equals $|{\bf u}\times{\bf v}|$
${\bf u}\times{\bf v}=\left|\begin{array}{lll}
{\bf i} & {\bf j} & {\bf k}\\
1 & 1 & 0\\
0 & 1 & 0
\end{array}\right|$
$=(0-0){\bf i}-(0-0){\bf j}+(1-0){\bf k}$
$={\bf k}$
Area = $|{\bf u}\times{\bf v}| = \sqrt{0+0+1}=1$
$ b.\quad$
Volume = $({\bf u}\times{\bf v} )\cdot{\bf w}\qquad $(triple scalar product)
We can calculate this as a determinant, but we already have ${\bf u}\times{\bf v}$, so
Volume $=0(1)+0(1)+1(1)$
$=1$
