Let \(\vec a,\;\vec b,\;\vec c\) be three vectors such that \(\vec a.\left( {\vec b + \vec c} \right) = \vec b.\left( {\vec c + \vec a} \right) = \vec c.\left( {\vec a + \vec b} \right) = 0\;and\;\left| {\vec a} \right| = 1,\;\left| {\vec b} \right| = 4,\;\left| {\vec c} \right| = 8\;then\;\left| {\vec a + \vec b + \vec c} \right|\) is: