In coordinate space, there are two points $\mathrm { A } ( 3,1,1 ) , \mathrm { B } ( 1 , - 3 , - 1 )$. For a point P on the plane $x - y + z = 0$, what is the minimum value of $| \overrightarrow { \mathrm { PA } } + \overrightarrow { \mathrm { PB } } |$? [4 points]\\
(1) $\frac { 4 \sqrt { 3 } } { 3 }$\\
(2) $\frac { 5 \sqrt { 3 } } { 3 }$\\
(3) $2 \sqrt { 3 }$\\
(4) $\frac { 7 \sqrt { 3 } } { 3 }$\\
(5) $\frac { 8 \sqrt { 3 } } { 3 }$