Step 1:
The vector equation of the line passing through the point (-9, 3, 4) and parallel to the vector (-1, 6, 0) is given by:
\[\textbf{r} = \begin{pmatrix} -9 \\ 3 \\ 4 \end{pmatrix} + \lambda \begin{pmatrix} -1 \\ 6 \\ 0 \end{pmatrix}\]
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