Let \(S\) be the set of all \((\lambda, \mu)\) for which the vectors \(\lambda \hat{i}-\hat{j}+\hat{k}, \hat{i}+2 \hat{j…

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

[JEE Main 2023, 15 Apr (Shift 1)]