$\textbf{k} = \frac{\pi}{a} \begin{bmatrix} d_x \\ d_y \\ d_z \end{bmatrix} $
$\textbf{k} \cdot \textbf{u}_\textbf{k} = $ 123
$| \textbf{k} \times \textbf{u}_\textbf{k}| = $ 456