If a line makes angles $120^{\circ}$ and $60^{\circ}$ with the positive directions of $X$ and $Z$ axes respectively,then the angle made by the line with the positive $Y$-axis is (in $^{\circ}$)

If a unit vector $\vec{r}$ makes angles $\frac{\pi}{3}$ with $\hat{i}$,$\frac{\pi}{4}$ with $\hat{j}$ and $\theta \in (0, \pi)$ with $\hat{k}$,then a value of $\theta$ is

Find the direction cosines and the length of a vector whose projections on the coordinate axes are $6, -3, 2$.

If $a, b, c$ are the direction ratios of a line $L$ and $\ell, m, n$ are its direction cosines,then $\frac{a^2}{b^2+c^2}=$

$A$ point $(x, y, z)$ moves parallel to the $xy$-plane. Which of the three variables $x, y, z$ remains fixed?

The angle $\theta$ between the lines whose direction cosines are $l_1 = \frac{-\sqrt{3}}{4}, m_1 = \frac{1}{4}, n_1 = \frac{-\sqrt{3}}{2}$ and $l_2 = \frac{-\sqrt{3}}{4}, m_2 = \frac{1}{4}, n_2 = \frac{\sqrt{3}}{2}$ is: (in $^{\circ}$)