$\begin{align} & \overrightarrow{BC}=\overrightarrow{C}-\overrightarrow{B}=-6\overrightarrow{i}\Rightarrow \overrightarrow{B}=\overrightarrow{C}+6\overrightarrow{i} \\ & \overrightarrow{B}=-2\overrightarrow{i}+4\overrightarrow{j}+6\overrightarrow{i}=4\overrightarrow{i}+4\overrightarrow{j} \\ & \overrightarrow{AB}=\overrightarrow{B}-\overrightarrow{A}=3\overrightarrow{i}-2\overrightarrow{j}\Rightarrow \overrightarrow{A}=\overrightarrow{B}-3\overrightarrow{i}+2\overrightarrow{j} \\ & \overrightarrow{A}=4\overrightarrow{i}+4\overrightarrow{j}-3\overrightarrow{i}+2\overrightarrow{j}=\overrightarrow{i}+6\overrightarrow{j} \\ \end{align}$