Vector Algebra

If \(\overline{\mathrm{a}}, \overline{\mathrm{b}} , \overline{\mathrm{c}}\) are three vectors which are perpendicular to \(\overline{\mathrm{b}}+\overline{\mathrm{c}}, \overline{\mathrm{c}}+\overline{\mathrm{a}}\) and \(\overline{\mathrm{a}}+\overline{\mathrm{b}}\) respectively, such that \(|\bar{a}|=2,|\bar{b}|=3,|\bar{c}|=4\), then \(|\bar{a}+\bar{b}+\bar{c}|=\)