If $\lambda>0$, let $\theta$ be the angle between the vectors $\vec{a}=\hat{\imath}+\lambda \hat{\jmath}-3 \hat{k}$ and $\vec{b}=3 \hat{\imath}-\hat{\jmath}+2 \hat{k}$. If the vectors $\vec{a}+\vec{b}$ and $\vec{a}-\vec{b}$ are mutually perpendicular, then the value of $(14 \cos \theta)^2$ is equal to