question_answer

\[{{L}_{1}}\] and \[{{L}_{2}}\] are two lines whose vector equations are \[{{L}_{1}}:\vec{r}=\lambda \,((cos\theta +\sqrt{3})\hat{i}+(\sqrt{2}sin\theta )\hat{j}+(cos\theta -\sqrt{3})\hat{k})\]\[{{L}_{2}}:\vec{r}=\mu (a\hat{i}+b\hat{j}+c\hat{k})\], where \[\lambda \]and \[\mu \]are scalars and \[\alpha \]is the acute angle between \[{{L}_{1}}\]and\[{{L}_{2}}\]. If the angle \[\alpha \]is independent of\[\theta \], then the value of \[\alpha \]is _____.

Answer:

\[(\pi /6)\]