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

If the direction cosines of a straight line are $\left(\frac{1}{c}, \frac{1}{c}, \frac{1}{c}\right)$,then $c$ is equal to

If $l_1, m_1, n_1$; $l_2, m_2, n_2$ and $l_3, m_3, n_3$ are the direction cosines of three mutually perpendicular lines,find the direction cosines of a line that makes equal angles with these lines.

Each of the angles $\beta$ and $\gamma$ that a given line makes with the positive $y-$ and $z-$axes,respectively,is half of the angle that this line makes with the positive $x-$axis. Then the sum of all possible values of the angle $\beta$ is

If the direction ratios of a line are $1, -3, 2$,find the direction cosines of the line.

$A$ line passes through the points $A(6, -7, -1)$ and $B(2, -3, 1)$. Find the direction cosines of the line such that the angle made by the line with the positive direction of the $x$-axis is acute.