The ratio in which (5, 4, –6) divides the line segment joining (3, 2, –4), (9, 8, –10) is

A point $\left(x,y,z\right)$ divides the linesegment joining the points $\left(x_1,y_1,z_1\right)$ and $\left(x_2,y_2,z_2\right)$ in the ratio $x_1-x:x-x_2$

Therefore, the ratio in which the point $\left(5,4,-6\right)$ divides the line segnment joining the points $\left(3,2,-4\right)$ and $\left(9,8,-10\right)$ is $\begin{array}{rcl}3-5:5-9& =& -2:-4=\boxed{\mathbf{1}\mathbf{:}\mathbf{2}}\end{array}$