If l2i+m2i+n2i=1 for i=1,2,3 & lilj+mimj+ninj=0 for i,j∈{1,2,3} and – InterviewSolution

1.	If l2i+m2i+n2i=1 for i=1,2,3 & lilj+mimj+ninj=0 for i,j∈{1,2,3} and i≠j and Δ=∣∣∣∣l1m1n1l2m2n2l3m3n3∣∣∣∣, then
Answer» If $l_{i}^{2} + m_{i}^{2} + n_{i}^{2} = 1$ for $i = 1, 2, 3$ & $l_{i} l_{j} + m_{i} m_{j} + n_{i} n_{j} = 0$ for $i, j \in {1, 2, 3}$ and $i \neq j$ and $Δ = ∣ ∣∣ ∣ \begin{matrix} l_{1} & m_{1} & n_{1} l_{2} & m_{2} & n_{2} l_{3} & m_{3} & n_{3} \end{matrix} ∣ ∣∣ ∣,$ then

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