Let $\widehat{i}, \widehat{j}$ and $\widehat{k}$ denote the standard unit vectors in $\mathbf{R}^3$ along the $x$-axis, $y$-axis and $z$-axis, respectively. Consider the sets
$\begin{aligned}<br/>X & =\{a \widehat{i}+b \widehat{j}+c \widehat{k}: a, b, c \in\{-1,0,1\}\} \text { and } \\<br/>Y & =\left\{\left(\vec{v}_1, \vec{v}_2, \vec{v}_3\right): \vec{v}_1, \vec{v}_2, \vec{v}_3 \in X \text { and } \vec{v}_1, \vec{v}_2, \vec{v}_3 \text { are mutually perpendicular unit vectors }\right\}<br/>\end{aligned}$
Then, the number of elements in $Y$ is

• A

  27
• B

  24
• C

  36
• Correct answer
  D

  48

Hence, the correct answer is option: 'D'.