Answer
$${\bf{r}}(t)
= \langle 3t,-t,-4t \rangle.$$
Work Step by Step
A vector parametrization for the given line is given by
$${\bf{r}}(t)= \langle 0,0,0 \rangle +t \langle 3,-1,-4 \rangle\\
= \langle 3t,-t,-4t \rangle.$$
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