Explanation

(d)
Given edges are
$\overrightarrow{\mathbf{a}} = \widehat{\dot{\mathbf{i}}} - \widehat{\mathbf{k}},\ \overrightarrow{\mathbf{b}} = \lambda\ \widehat{\dot{\mathbf{i}}} + \widehat{\dot{\mathbf{j}}} + (1 - \lambda)\widehat{\mathbf{k}}$
$and\ \overrightarrow{\mathbf{c}} = \mu\ \widehat{\dot{\mathbf{i}}} + \lambda\ \widehat{\dot{\mathbf{j}}} + (1 + \lambda - \mu)\widehat{\mathbf{k}}$
$\therefore$ Volume of parallelopiped
$= \left\lbrack \overrightarrow{\mathbf{a}}\ \overrightarrow{\mathbf{b}}\ \overrightarrow{\mathbf{c}} \right\rbrack$
$= \left| \begin{matrix}
1 & 0 & - 1 \\
\lambda & 1 & 1 - \lambda \\
\mu & \lambda & 1 + \lambda - \mu
\end{matrix} \right|$
$= 1\left( 1 + \lambda - \mu - \lambda + \lambda^{2} \right) - 0 - 1\left( \lambda^{2} - \mu \right)$
$= 1 + \lambda^{2} - \mu - \lambda^{2} + \mu = 1$
Hence, volume depends on neither λ nor μ.