For given vectors, \[\overrightarrow{a}=2\widehat{i}-\widehat{j}+2\widehat{k}\] and \[\overrightarrow{b}=-\widehat{i}+\widehat{j}-\widehat{k}\], find the unit vector in the direction of the vector \[\overrightarrow{a}+\overrightarrow{b}\]