The point $\left( \frac{1}{2}, -\frac{13}{4} \right)$ divides the line segment joining the points $(3, -5)$ and $(-7, 2)$ in the ratio of:

The points $(a, b)$,$(c, d)$,and $\left( \frac{kc + la}{k + l}, \frac{kd + lb}{k + l} \right)$ are:

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:

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

If $A(4,3,2), B(5,4,6), C(-1,-1,5)$ are the vertices of a triangle,then the coordinates of the point in which the bisector of the angle $A$ meets the side $BC$ is

The coordinates of the point which divides the line joining the points $(2, 3, 4)$ and $(3, -4, 7)$ in the ratio $2:4$ externally are: