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 $PQ =$

The ratio in which the line joining the points $(2, 4, 5)$ and $(3, 5, -4)$ is divided by the $yz$-plane is

If the coordinates of the vertices of a $\triangle ABC$ are $A(7,6,4)$,$B(5,4,6)$,$C(3,2,0)$ and the bisector of $\angle BAC$ meets the side $BC$ at $D$,then the coordinates of $D$ are

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

Find the coordinates of the point which divides the line segment joining the points $(1, -2, 3)$ and $(3, 4, -5)$ in the ratio $2:3$ internally.

$A(3, 2, -1), B(4, 1, 0), C(2, 1, 4)$ are the vertices of a triangle $ABC$. If the bisector of $\angle BAC$ intersects the side $BC$ at $D(p, q, r)$,then $\sqrt{2p + q + r} =$