Answer
$Q = \left( {5,5,4} \right)$
Work Step by Step
The vector ${\bf{v}} = \overrightarrow {RQ} $ is based at $R$ and has the head at $Q$, so
${\bf{v}} = \overrightarrow {RQ} = Q - R = Q - \left( {1,4,3} \right) = \left( {4,1,1} \right)$
$Q = \left( {5,5,4} \right)$