Given that $P _ { 1 } , P _ { 2 } , Q _ { 1 } , Q _ { 2 } , R$ are five distinct points on a plane, where $P _ { 1 } , P _ { 2 } , R$ are not collinear, and satisfy $\overrightarrow { P _ { 1 } R } = 4 \overrightarrow { P _ { 1 } Q _ { 1 } }$ and $\overrightarrow { P _ { 2 } R } = 7 \overrightarrow { P _ { 2 } Q _ { 2 } }$, then $\overrightarrow { Q _ { 1 } Q _ { 2 } } =$ (15-1) $\overrightarrow { P _ { 1 } Q _ { 1 } } +$ (15-2)(15-3) $\overrightarrow { P _ { 2 } Q _ { 2 } }$.