Two forces \(\vec{F}_1\) and \(\vec{F}_2\) are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between \(\vec{F}_1\) and \(\vec{F}_2\) is \(\cos^{-1}\left(\frac{1}{n}\right).\) The value of |n| is ____