Find the ratio in which the line segment joining the points $(4, 8, 10)$ and $(6, 10, -8)$ is divided by the $YZ$-plane.

If the $x$-coordinate of a point $P$ on the line joining the points $Q(2,2,1)$ and $R(5,1,-2)$ is $4$,then the $z$-coordinate of $P$ is

The ratio in which $B\left(\frac{33}{5}, \frac{28}{5}, \frac{38}{5}\right)$ divides the line segment joining $A(3, 2, 4)$ and $C(9, 8, 10)$ is

The coordinates of the point which divides the line joining the points $(2, 3, 4)$ and $(3, -4, 7)$ in the ratio $2:4$ externally are:

$A(1, 2, 3)$,$B(2, 3, 1)$,and $C(3, 1, 2)$ are three points. If the point $P$ divides $AB$ in the ratio $1:2$ and the point $Q$ divides $BC$ in the ratio $-2:3$,then the distance between $P$ and $Q$ is

The harmonic conjugate of $(2,3,4)$ with respect to the points $(3,-2,2)$ and $(6,-17,-4)$ is