The ratio in which the point $P$,whose abscissa is $3$,divides the line segment joining $A(6, 5)$ and $B(-1, 4)$ is equal to .........

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

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 $k$?

If the point $(3,4,5)$ divides the line segment joining the points $(1,2,3)$ and $(4,5,6)$ in the ratio $\lambda: 1$,then the point which divides the line segment joining the points $(3,4,5)$ and $(1,2,3)$ in the ratio $-1: \lambda$ is

The ratio in which the line joining the points $(a, b, c)$ and $(-a, -c, -b)$ is divided by the $xy$-plane is

Show that the points $A (1,-2,-8), B (5,0,-2)$ and $C (11,3,7)$ are collinear,and find the ratio in which $B$ divides $AC$.