If a line makes angles $\alpha, \beta, \gamma$ with the positive directions of $X, Y$ and $Z$-axes respectively,then the value of $\sin ^2 \alpha+\sin ^2 \beta+\sin ^2 \gamma=$

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

If a line $L$ makes angles $\frac{\pi}{3}$ and $\frac{\pi}{4}$ with the positive $X$-axis and positive $Y$-axis respectively,then the angle made by $L$ with the positive direction of $Z$-axis is

$A$ space vector makes the angles $150^{\circ}$ and $60^{\circ}$ with the positive direction of $x$- and $y$-axes. The angle made by the vector with the positive direction of the $z$-axis is (in $^{\circ}$)

If the direction cosines of two lines are such that $2l + m + 2n = 0$ and $3l^2 + 5m^2 - 11n^2 = 0$,then the angle between the two lines is

The direction cosines of a line are $\langle \frac{-9}{11}, \frac{6}{11}, \frac{-2}{11} \rangle$ respectively. Then its direction ratios are