Let S be the set of all (lamda, mu) for ...

Let S be the set of all `(lamda, mu)` for which the vectors `lamda hati-hatj+hatk , hati+2hatj+mu hatk and 3hati-4hatj+5hatk`, where `lamda-mu=5`, are coplanar, then `sum_((lamda,mu)in S) 80(lamda^2 + mu^2)` is equal to

A

2210

B

2370

C

2130

D

2290

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