Mathematics - Vector Question with Solution | TestHub

$$\begin{array}{rl}& \overrightarrow{\mathrm{PA}}+\overrightarrow{\mathrm{AC}}+\overrightarrow{\mathrm{CP}}=0\\ & \overline{\mathrm{PB}}+\overrightarrow{\mathrm{BC}}+\overrightarrow{\mathrm{CP}}=0\end{array}$$ Adding, we get $$\overrightarrow{\mathrm{PA}}+\overrightarrow{\mathrm{PB}}+\overrightarrow{\mathrm{AC}}+\overrightarrow{\mathrm{BC}}+2\overrightarrow{\mathrm{CP}}=0$$ Since $\overrightarrow{AC}=-\overrightarrow{BC}$ $$\begin{array}{rl}& \&\overrightarrow{\mathrm{CP}}=-\overrightarrow{\mathrm{PC}}\\ & \Rightarrow \overrightarrow{\mathrm{PA}}+\overrightarrow{\mathrm{PB}}-2\overrightarrow{\mathrm{PC}}=0.\end{array}$$