$XOZ$-plane divides the line segment joining the points $(2, 3, 1)$ and $(6, 7, 1)$ in the ratio: (in $: 7$)

If $z_1$ and $z_2$ are the $z$-coordinates of the points of trisection of the line segment joining the points $A(2, 1, 4)$ and $B(-1, 3, 6)$,then $z_1 + z_2 =$

The point which divides the line segment joining the points $(2, 4, 5)$ and $(3, 5, -4)$ in the ratio $-2 : 3$ lies on which of the following?

Find the coordinates of the point which divides the line segment joining the points $(-2, 3, 5)$ and $(1, -4, 6)$ in the ratio $2:3$ internally.

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

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