JEE MATHEMATICS MCQ: DOT PRODUCT OF VECTORS

$L_1$ and $L_2$ are two lines whose vector equations are
$L_1: \mathbf{r}=\lambda[(\cos \theta+\sqrt{3}) \mathbf{i}+(\sqrt{2} \sin \theta) \mathbf{j}+(\cos \theta-\sqrt{3}) \mathbf{k}]$
and $L_2: \mathbf{r}=\mu(a \mathbf{i}+b \mathbf{j}+c \mathbf{k})$
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