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 the $yz$-plane divides the line segment joining the points $(-3, 4, -2)$ and $(2, 1, 3)$ is:

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 $k$?

Points $A(3, 2, 4)$, $B\left(\frac{33}{5}, \frac{28}{5}, \frac{38}{5}\right)$ and $C(9, 8, 10)$ are given. The ratio in which $B$ divides $\overline{AC}$ 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

If the orthocenter and circumcenter of a triangle are $(3, -4, 2)$ and $(2, 1, 3)$ respectively,then its centroid is