Answer
$${\bf{r}}(t)= \langle 4t, t,t \rangle.$$
Work Step by Step
To find a vector parametrization for the given line, we have to find the direction vector:
$(4,1,1 )-(0,0,0)=\langle 4,1,1 \rangle $
Hence, we get the parametrization $${\bf{r}}(t)= \langle 0,0,0 \rangle +t \langle 4,1,1 \rangle\\ = \langle 4t, t,t \rangle.$$
