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 ________.
