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 point $\left( \frac{1}{2}, -\frac{13}{4} \right)$ divides the line segment joining the points $(3, -5)$ and $(-7, 2)$ in the ratio of:

If $P(-3, -2, 4)$,$Q(-9, -8, 10)$,and $R(-5, -4, 6)$ are collinear,then the ratio in which $R$ divides $PQ$ is

If the line joining $A(1,3,4)$ and $B$ is divided by the point $P(-2,3,5)$ in the ratio $1:3$,then the coordinates of $B$ are:

Point $A$ divides the line segment joining points $(-5, 1)$ and $(3, 5)$ in the ratio $k:1$. If the coordinates of points $B$ and $C$ are $(1, 5)$ and $(7, -2)$ respectively,and the area of $\Delta ABC$ is $2$ square units,what is the value of $k$?

If $A(2,-1,1)$,$B(2,5,1)$,and $C(0,-2,3)$ are the vertices of a triangle,and $D$ is the point of intersection of the side $BC$ and the internal angular bisector of angle $A$,then $AD=$