Ta có: $\overrightarrow{AJ} =\overrightarrow{BI}=-\overrightarrow{IB}$
$\overrightarrow{CS} =-\overrightarrow{RA}$
$\overrightarrow{PC} =-\overrightarrow{BQ}$
=> $\overrightarrow{RJ} +\overrightarrow{IQ}+\overrightarrow{PS}
= $(\overrightarrow{RA} +\overrightarrow{AJ})+(\overrightarrow{IB}+\overrightarrow{BQ})(\overrightarrow{PC}+\overrightarrow{CS})$
= $(\overrightarrow{RA} +\overrightarrow{-IB})+(\overrightarrow{IB}+\overrightarrow{-PC})+(\overrightarrow{PC}+\overrightarrow{-RA})$
= $(\overrightarrow{IB} +\overrightarrow{-IB})+(\overrightarrow{PC}+\overrightarrow{-PC})+(\overrightarrow{RA}+\overrightarrow{-RA})=\overrightarrow{0}$ ( đpcm )