Explanation

(b)
Given, $\overrightarrow{\mathbf{OA}} = 2\widehat{\dot{\mathbf{i}}} - 2\widehat{\dot{\mathbf{j}}} + \widehat{\mathbf{k}}$
$\overrightarrow{\mathbf{OB}} = 5\widehat{\dot{\mathbf{i}}} - 4\widehat{\dot{\mathbf{j}}} + 4\widehat{\mathbf{k}}$
$and\ \overrightarrow{\mathbf{OC}} = \widehat{\dot{\mathbf{i}}} - 2\widehat{\dot{\mathbf{j}}} + 4\widehat{\mathbf{k}}$
volume of parallelopiped
$= \left\lbrack \overrightarrow{\mathbf{OA}}\ \overrightarrow{\mathbf{OB}}\ \overrightarrow{\mathbf{OC}} \right\rbrack$
$= \left| \begin{matrix}
2 & - 2 & 1 \\
5 & - 4 & 4 \\
1 & - 2 & 4
\end{matrix} \right|$
$= 2( - 16 + 8) + 2(20 - 4) + 1( - 10 + 4)$
$= 10\$cu units