Find a unit vector perpendicular to each of the vector \[\overrightarrow{a}+\overrightarrow{b}\] and \[\overrightarrow{a}-\overrightarrow{b}\], where \[\overrightarrow{a}=3\widehat{i}+2\widehat{j}+2\widehat{k}\] and \[\overrightarrow{b}=\widehat{i}+2\widehat{j}-2\widehat{k}\].