Three vectors $\overrightarrow{P},\overrightarrow{Q}and\overrightarrow{R}$ are such that $\left|\overrightarrow{Q}\right|=A\sqrt{2}$ and the angle between $\overrightarrow{P}and\overrightarrow{Q}\text{, }\overrightarrow{Q}and\overrightarrow{R}\text{, }\overrightarrow{R}and\overrightarrow{P}$ are ${90}^0,{150}^0,{120}^0$ respectively. Find the value of $\left|\overrightarrow{P}\right|:$