The number of straight lines that are equally inclined to the three-dimensional coordinate axes is

If a line $L$ makes angles $\pi / 3$ and $\pi / 4$ with $Y$-axis and $Z$-axis respectively,then the angle between $L$ and another line having direction ratios $(1, 1, 1)$ is

Find the direction cosines of a line which makes equal angles with the coordinate axes.

The direction cosines of the line passing through $P(2, 3, -1)$ and the origin are

Let $P(x, y, z)$ be a point in the first octant,whose projection in the $xy$-plane is the point $Q$. Let $OP = \gamma$; the angle between $OQ$ and the positive $x$-axis be $\theta$; and the angle between $OP$ and the positive $z$-axis be $\phi$,where $O$ is the origin. Then the distance of $P$ from the $x$-axis is:

If the direction cosines of two lines are given by $l+m+n=0$ and $l^2-5m^2+n^2=0$, then the angle between them is