The ratio in which the point $(5, -2)$ divides the line segment joining the points $(8, 4)$ and $(9, 6)$ is:

If $A(4,3,5)$,$B(0,-2,2)$,and $C(3,2,1)$ are three points,then the coordinates of the point $D$ where the bisector of $\angle BAC$ meets the side $BC$ are:

Let $P(\alpha, 4, 7)$ and $Q(3, \beta, 8)$ be two points. If the $YZ$-plane divides the line segment joining $P$ and $Q$ in the ratio $2:3$ and the $ZX$-plane divides the line segment joining $P$ and $Q$ in the ratio $4:5$,then the length of the line segment $PQ$ 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 harmonic conjugate of $(2,3,4)$ with respect to the points $(3,-2,2)$ and $(6,-17,-4)$ is

Let $A(4,3,5), B(1,-2,1), C(3,2,1)$ be the vertices of a triangle $ABC$. If the internal bisector of $\angle BAC$ meets the side $BC$ at $D$, then $CD=$