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 $A(3, 2, -4)$ and $B(9, 8, -10)$ be two points. Let $P_1$ divide $AB$ in the ratio $1:2$ and $P_2$ divide $AB$ in the ratio $2:1$. If the point $P(\alpha, \beta, \gamma)$ divides $P_1 P_2$ in the ratio $1:1$, then $\alpha + 2\beta + 2\gamma =$

Given that $P(3, 2, -4)$,$Q(5, 4, -6)$,and $R(9, 8, -10)$ are collinear. Find the ratio in which $Q$ divides $PR$.

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

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 ratio in which the $YZ$-plane divides the line segment formed by joining the points $(-2, 4, 7)$ and $(3, -5, 8)$.