Let S be the set of all (λ, μ) for which the vectors λ i - j + k, i +2 j +μ k and 3 i -4 j +5 k, where λ-μ=5, are coplanar, then Σ_(λ, μ) ∈ S…

Let $\displaystyle S$ be the set of all $\displaystyle (\lambda, \mu)$ for which the vectors $\displaystyle \lambda \hat{i}-\hat{j}+\hat{k}, \hat{i}+2 \hat{j}+\mu \hat{k}$ and $\displaystyle 3 \hat{i}-4 \hat{j}+5 \hat{k}$, where $\displaystyle \lambda-\mu=5$, are coplanar, then $\displaystyle \sum_{(\lambda, \mu) \in S} 80\left(\lambda^2+\mu^2\right)$ is equal to