3 A surface, \(S\), is defined by \(g ( x , y , z ) = 0\) where \(g ( x , y , z ) = 2 x ^ { 3 } - x ^ { 2 } y + 2 x y ^ { 2 } + 27 z\). The normal to \(S\) at the point \(\left( 1,1 , - \frac { 1 } { 9 } \right)\) and the tangent plane to \(S\) at the point \(( 3,3 , - 3 )\) intersect at \(P\). Determine the position vector of P .