Coplanar Vectors Sum

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

∑

^{(λ, μ) ϵ S}

80 (λ² + μ²) is equal to

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