If a line makes angles $\alpha, \beta, \gamma$ with the coordinate axes, then the sum of values of $\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma$ and $\cos 2\alpha + \cos 2\beta + \cos 2\gamma$ is ...

If a line makes angles $\alpha, \beta, \gamma$ with the coordinate axes and $\cos \alpha = 14/15, \cos \beta = 1/3$,then $\cos \gamma = \dots$

In three-dimensional space,a line $AB$ makes angles of $45^\circ$ and $120^\circ$ with the positive $x$-axis and $y$-axis,respectively. If $AB$ makes an acute angle $\theta$ with the positive $z$-axis,then $\theta = \dots^\circ$.

The angle between the lines with direction ratios $3, 4, 5$ and $4, -3, 5$ is equal to ......... $^o$.

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

If the projections of the line segment $\overrightarrow{AB}$ on $XY$,$YZ$,and $ZX$ planes are $\sqrt{15}$,$\sqrt{46}$,and $7$ respectively,then the projection of $\overrightarrow{AB}$ on the $y$-axis is