The octant in which the point $(2, -4, -7)$ lies is

If $l, m, n$ are the direction cosines of a line that is perpendicular to the lines having the direction ratios $1, 2, -1$ and $1, -2, 1$,then $(l+m+n)^2=$

If a line makes an angle of $\frac{\pi}{3}$ with each $X$ and $Y$ axis,then the acute angle made by $Z$-axis is

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 ratios are proportional to $(1, 2, 1)$ and $(2, -3, 6)$ is

If the angle between the lines whose direction ratios are $2, -1, 2$ and $a, 3, 5$ is $45^\circ$,then $a =$