Answer
$Q = \left( {1,2,1} \right)$
Work Step by Step
The vector ${\bf{v}}$ in the form $\overrightarrow {PQ} $ is based at $P = \left( {0,1,1} \right)$ and has the head at $Q$. So,
${\bf{v}} = \overrightarrow {PQ} = Q - \left( {0,1,1} \right) = \left( {1,1,0} \right)$
$Q = \left( {1,2,1} \right)$.