The harmonic conjugate of the point $P(2,3,4)$ with respect to the points $A(3,-2,2)$ and $B(6,-17,-4)$ is

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 $z_1 + z_2 =$

If $A(4,3,5)$,$B(0,-2,2)$,and $C(3,2,1)$ are three points,then the coordinates of the point $D$ where the bisector of $\angle BAC$ meets the side $BC$ are:

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

Using the section formula,show that the points $A(2, -3, 4)$,$B(-1, 2, 1)$,and $C(0, \frac{1}{3}, 2)$ are collinear.

If the point $(a, 8, -2)$ divides the line segment joining the points $(1, 4, 6)$ and $(5, 2, 10)$ in the ratio $m: n$,then $\frac{2m}{n} - \frac{a}{3} =$