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

If the angles made by a straight line with the coordinate axes are $\alpha, \frac{\pi}{2}-\alpha, \beta$, then $\beta$ is equal to

$A$ line makes the same angle $\theta$ with each of the $x$ and $z$-axes. If the angle $\beta$,which it makes with the $y$-axis,is such that $\sin^2 \beta = 3 \sin^2 \theta$,then $\cos^2 \theta$ equals:

Find the projection of the line segment joining the points $(-1, 0, 3)$ and $(2, 5, 1)$ on a line whose direction ratios are $6, 2, 3$.

$A$ line $AB$ in three dimensions makes angles $45^{\circ}$ and $120^{\circ}$ with the positive $X$-axis and the positive $Y$-axis respectively. If $AB$ makes an acute angle $\theta$ with the positive $Z$-axis,then $\theta$ equals (in $^{\circ}$)

$A$ vector makes equal angles $\alpha$ with $x$ and $y$ axes and $90^{\circ}$ with $z$-axis. Then $\alpha=$