If $P$ divides the line segment joining the points $A(1, 2, -1)$ and $B(-1, 0, 1)$ externally in the ratio $1: 2$ and $Q = (1, 3, -1)$,then $PQ =$

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 $m:n$ is the ratio in which the point $\left(\frac{8}{5}, -\frac{1}{5}, \frac{8}{5}\right)$ divides the line segment joining the points $(2, p, 2)$ and $(p, -2, p)$, where $p$ is an integer, then $\frac{3m+n}{3n} =$

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

If $A(1, 2, 0)$,$B(2, 0, 1)$,and $C(-3, 0, 2)$ are the vertices of $\triangle ABC$,then the length of the internal bisector of $\angle BAC$ is

The ratio in which the $yz$-plane divides the line segment joining $(-3, 4, -2)$ and $(2, 1, 3)$ is