MathematicsHard202×since 2002Q5752Let the position vectors of the points A, B, C and D be 5i^+5j^+2λk^,i^+2j^+3k^,−2i^+λj^+4k^5 \hat{i}+5 \hat{j}+2 \lambda \hat{k}, \hat{i}+2 \hat{j}+3 \hat{k},-2 \hat{i}+\lambda \hat{j}+4 \hat{k}5i^+5j^+2λk^,i^+2j^+3k^,−2i^+λj^+4k^ and −i^+5j^+6k^-\hat{i}+5 \hat{j}+6 \hat{k}−i^+5j^+6k^. Let the set S={λ∈RS=\{\lambda \in \mathbb{R}S={λ∈R : the points A, B, C and D are coplanar }\}}. Then \sum_\limits{\lambda \in S}(\lambda+2)^{2} is equal to :A372\frac{37}{2}237B25C13D41Check answerSkip