\(∆ABC \)外接圆圆心为\(O\)，半径为\(1\)，\(2 \overrightarrow{AO}= \overrightarrow{AB}+ \overrightarrow{AC} \)且\(\left| \overrightarrow{OA}\right|=\left| \overrightarrow{AB}\right| \)，则向量\(\overrightarrow{BA} \)在\(\overrightarrow{BC} \)方向上的投影为_______．