vectors

Vectors:

$\begin{array}{|lrcll|} \hline (1) & a+b &=& RS \\\\ (2) & 2a+2b+BA &=& 2c \\ & BA &=& 2\left(c-(a+b)\right) \\\\ (3) & c+PQ - \dfrac{BA}{2} &=& 2(a+b) \\ &c+PQ- \dfrac{2\left(c-(a+b)\right)}{2} &=& 2(a+b) \\ &c+PQ- \left(c-(a+b) \right) &=& 2(a+b) \\ &c+PQ-c+(a+b) &=& 2(a+b) \\ &PQ +(a+b) &=& 2(a+b) \\ &PQ &=& 2(a+b)-(a+b) \\ &PQ &=& a+b \quad & | \quad a+b = RS \\ &\mathbf{PQ} & \mathbf{=} & \mathbf{RS} \\ \hline \end{array}$