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MCQMediumJEE Main 2023 · 15 April, Shift 1Cross Product

Mathematics Question from JEE Main 2023 · 15 April, Shift 1

Let SS be the set of all (λ,μ)(\lambda,\mu) for which the vectors

λi−j+k,i+2j+μk,and3i−4j+5k\lambda \mathbf{i}-\mathbf{j}+\mathbf{k},\quad \mathbf{i}+2\mathbf{j}+\mu\mathbf{k}, \quad \text{and} \quad 3\mathbf{i}-4\mathbf{j}+5\mathbf{k}

where λ−μ=5\lambda-\mu=5, are coplanar. Then

∑(λ,μ)∈S80(λ2+μ2)\sum_{(\lambda,\mu)\in S} 80(\lambda^2+\mu^2)

is equal to

  • A

    21302130

  • B

    22102210

  • C

    22902290

  • D

    23702370

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