As shown in the figure, let $\mathrm { F } , \mathrm { F } ^ { \prime }$ be the two foci of the hyperbola $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 9 } = 1$. For point P on the hyperbola in the first quadrant and point Q on the hyperbola in the second quadrant, when $\overline { \mathrm { PF } ^ { \prime } } - \overline { \mathrm { QF } ^ { \prime } } = 3$, find the value of $\overline { \mathrm { QF } } - \overline { \mathrm { PF } }$. [3 points]