If \( l_{\mathrm{i}}^{2}+m_{\mathrm{i}}^{2}+n_{\mathrm{i}}^{2}=1 \) and \( l_{\mathrm{i}} l_{\ma...
If \( l_{\mathrm{i}}^{2}+m_{\mathrm{i}}^{2}+n_{\mathrm{i}}^{2}=1 \) and \( l_{\mathrm{i}} l_{\mathrm{j}}+m_{\mathrm{i}} m_{\mathrm{j}}+n_{\mathrm{i}} n_{\mathrm{j}}=0 \forall \mathrm{i}, \mathrm{j} \in\{1,2,3\} \), \( i \neq j \) and \( \Delta=\left|\begin{array}{lll}l_{1} & m_{1} & n_{1} \\ l_{2} & m_{2} & n_{2} \\ l_{3} & m_{3} & n_{3}\end{array}\right| \) then
(a) \( |\Delta|=3 \)
(b) \( |\Delta|=2 \)
(c) \( |\Delta|=1 \)
(d) \( \Delta=0 \)
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