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 $B\left(\frac{33}{5}, \frac{28}{5}, \frac{38}{5}\right)$ divides the line segment joining $A(3, 2, 4)$ and $C(9, 8, 10)$ is

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:

Find the coordinates of the centroid of the triangle whose vertices are $(x_{1}, y_{1}, z_{1}), (x_{2}, y_{2}, z_{2})$ and $(x_{3}, y_{3}, z_{3})$.

The point dividing the line segment joining $(3, -2, 1)$ and $(-2, 3, 11)$ in the ratio $2:3$ is

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