$A$ line makes angles $\alpha, \beta, \gamma$ with the coordinate axes. If $\alpha + \beta = 90^\circ$,then $\gamma = \dots \dots ^\circ$.

$A$ line passes through the points $A (6, -7, -1)$ and $B (2, -3, 1)$. Find the direction cosines of the line such that the angle $\alpha$ made with the $x$-axis is acute.

If the direction ratios $(d.r.'s)$ of two lines are connected by the relations $a-b+c=0$ and $a^2-b^2+2c^2=0$, and $\theta$ is the angle between these lines, then $\cos \theta = $

The perpendicular distance of the point $P(6, 7, 8)$ from the $XY$-plane is:

The direction cosines of two lines are $\langle\frac{\sqrt{3}}{2}, \frac{1}{4}, \frac{\sqrt{3}}{4}\rangle$ and $\langle-\frac{\sqrt{3}}{2}, \frac{1}{4}, \frac{\sqrt{3}}{4}\rangle$. Then the angle between the lines is equal to (in $^{\circ}$)

If a vector $\vec{r}$ with direction cosines $l, m, n$ is equally inclined to the coordinate axes, then the total number of such vectors is