Answer
${\bf{r}}{\rm{'''}}\left( t \right) = \left( {6,0,0} \right)$
Work Step by Step
We have ${\bf{r}}\left( t \right) = \left( {{t^3},4{t^2},7t} \right)$. So,
${\bf{r}}'\left( t \right) = \left( {3{t^2},8t,7} \right)$
${\bf{r}}{\rm{''}}\left( t \right) = \left( {6t,8,0} \right)$
${\bf{r}}{\rm{'''}}\left( t \right) = \left( {6,0,0} \right)$
