Fill in the blanks:
Coordinate planes divide the space into ........ octants.

If a line makes angles $\alpha, \beta, \gamma$ with the positive direction of $x, y$ and $z$-axis respectively,then $\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma$ is equal to:

The angle between the lines whose direction ratios satisfy the equations $l+m+n=0$ and $l^2=m^2+n^2$ is

Direction cosines of the line $\frac{x+2}{2} = \frac{2y-5}{3}, z = -1$ are $.......$

If $OA$ is equally inclined to $OX, OY$ and $OZ$ and if $A$ is $\sqrt{3}$ units from the origin,then $A$ is:

Show that the three lines with direction cosines $\frac{12}{13}, \frac{-3}{13}, \frac{-4}{13} ; \frac{4}{13}, \frac{12}{13}, \frac{3}{13} ; \frac{3}{13}, \frac{-4}{13}, \frac{12}{13}$ are mutually perpendicular.