For λ>0, let θ be the angle between the vectors a = i +λ j -3 k and b =3 i - j +2 k. If the vectors a + b and a - b are mutually perpendicular, then…

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