\overrightarrow{SP} = \frac{1}{2} \overrightarrow{RP} = \frac{1}{2} \left( \overrightarrow{RA} + \overrightarrow{AP} \right) = \frac{1}{2} \overrightarrow{a} - \frac{1}{2} \overrightarrow{b}