Find the locus of a point such that the sum of its distances from the $xy$-plane and the $yz$-plane is equal to its distance from the $zx$-plane.

If the direction cosines of two lines are such that $2l + m + 2n = 0$ and $3l^2 + 5m^2 - 11n^2 = 0$,then the angle between the two lines is

$A$ ray makes angles $\frac{\pi}{3}$ and $\frac{\pi}{4}$ with $Y$ and $Z$-axes respectively. Then,the value of the sine of the angle made by the ray with $X$-axis is

If a line makes angles $\frac{\pi}{3}$ and $\frac{\pi}{4}$ with the $X$-axis and $Y$-axis respectively,then the angle made by the line with the $Z$-axis is

If the direction cosines of two lines are $(\frac{2}{3}, \frac{2}{3}, \frac{1}{3})$ and $(\frac{5}{13}, \frac{12}{13}, 0)$,then identify the direction ratios of a line which is bisecting one of the angles between them.

The projections of a vector on the three coordinate axes are $6, -3, 2$ respectively. The direction cosines of the vector are . . . . . . .