If the projections of a line on the coordinate axes are $2, -1, 2$,then the length of the line is

If the relation between the direction ratios of two lines in $\mathbb{R}^3$ are given by $l+m+n=0$ and $2lm+2mn-ln=0$, then the angle between the lines is ($l, m, n$ have their usual meaning).

$A$ line makes angles of $45^\circ$ and $60^\circ$ with the positive axes of $X$ and $Y$ respectively. The angle made by the same line with the positive axis of $Z$ is:

$A$ point on the $XOZ$-plane divides the line segment joining the points $(5, -3, -2)$ and $(1, 2, -2)$ at:

$E(1,0,0), F(0,2,0), G(0,0,3)$ are respectively the mid-points of the sides $AB, BC, CA$ of $\triangle ABC$. If $a_1, b_1, c_1$ and $a_2, b_2, c_2$ are respectively the direction ratios of $AF$ and $BG$, then $\frac{a_1^2+b_1^2+c_1^2}{a_2^2+b_2^2+c_2^2}=$

$A$ line makes angles $60^{\circ}, 45^{\circ}, \theta$ with positive $X, Y, Z$-axes respectively. If $\theta$ is an acute angle, then $\tan \theta=$