The perpendicular distance of the point $P(6, 7, 8)$ from the $XY$-plane is:

If a line makes angles of measure $\frac{\pi}{6}$ and $\frac{\pi}{3}$ with $X$ and $Y$ axes respectively,then the angle made by the line with $Z$ axis is

If a line makes angles $\alpha, \beta, \gamma$ with the positive directions of $X, Y$ and $Z$-axes respectively,then the value of $\sin ^2 \alpha+\sin ^2 \beta+\sin ^2 \gamma=$

Which of the following can not be the direction cosines of a line?

$A$ line makes the same angle $\theta$ with each of the $x$ and $z$-axes. If the angle $\beta$,which it makes with the $y$-axis,is such that $\sin^2 \beta = 3 \sin^2 \theta$,then $\cos^2 \theta$ equals:

If the direction ratios of a line are proportional to $1, 2, 3$,find the projection of the line segment joining the points $(5, 2, 3)$ and $(-1, 0, 2)$ on the line.