Answer
$P = \left( { - 2,6,0} \right)$
Work Step by Step
The vector ${\bf{w}} = \overrightarrow {PR} $ is based at $P$ and has the head at $R$, so
${\bf{w}} = \overrightarrow {PR} = R - P = \left( {1,4,3} \right) - P = \left( {3, - 2,3} \right)$
$P = \left( { - 2,6,0} \right)$