If $\alpha, \beta, \gamma$ are the angles that a line makes with the positive direction of the coordinate axes,then $\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma = $

If a line makes angles $\alpha, \beta, \gamma$ with the coordinate axes,then $\cos 2\alpha + \cos 2\beta + \cos 2\gamma = \dots$

$A$ line in the $3-$dimensional space makes an angle $\theta \left( 0 < \theta \le \frac{\pi}{2} \right)$ with both the $x$ and $y$ axes. Then the set of all values of $\theta$ is the interval

Each of the angles $\beta$ and $\gamma$ that a given line makes with the positive $y-$ and $z-$axes,respectively,is half of the angle that this line makes with the positive $x-$axis. Then the sum of all possible values of the angle $\beta$ is

The angle between the lines whose direction cosines $(\ell, m, n)$ satisfy the equations $\ell+m+n=0$ and $\ell^2+m^2-n^2=0$ is:

Name the octants in which the following points lie:
$(1, 2, 3), (4, -2, 3), (4, -2, -5), (4, 2, -5), (-4, 2, -5), (-4, 2, 5), (-3, -1, 6), (-2, -4, -7)$