Vector Algebra

For \(\lambda>0\), let \(\theta\) be the angle between the vectors \(\vec{a}=\hat{i}+\lambda \hat{j}-3 \hat{k}\) and \(\vec{b}=3 \hat{i}-\hat{j}+2 \hat{k}\). 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