If the direction ratios $(l, m, n)$ of two lines satisfy the equations $l+m+n=0$ and $mn-2ln+lm=0$, then the angle between the lines is

$A$ line in the $3-$dimensional space makes an angle $\theta \left( 0 < \theta \le \frac{\pi}{2} \right)$ with both the $x$ and $y$ axes. Then the set of all values of $\theta$ is the interval

The projection of the line segment joining $P(2, -1, 0)$ and $Q(3, 2, -1)$ on the line whose direction ratios are $1, 2, 2$ is

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 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 projections of a line on the coordinate axes are $4, 6, 12$,what are the direction cosines of the line?