If the points $A(9, 8, -10)$,$B(3, 2, -4)$ and $C(5, 4, -6)$ are collinear,then the point $C$ divides the line segment $AB$ in the ratio:

Find the coordinates of the centroid of the triangle whose vertices are $(x_{1}, y_{1}, z_{1}), (x_{2}, y_{2}, z_{2})$ and $(x_{3}, y_{3}, z_{3})$.

If the line joining $A(1,3,4)$ and $B$ is divided by the point $P(-2,3,5)$ in the ratio $1:3$,then the coordinates of $B$ are:

If the centroid of a tetrahedron $OABC$ is $(1, 2, -1)$, where $O$ is the origin, $A(a, 2, 3)$, $B(1, b, 2)$, and $C(2, 1, c)$ are the other vertices, then the distance of the point $P(a, b, c)$ from the origin is...

Using the section formula,prove that the three points $A(-4, 6, 10)$,$B(2, 4, 6)$,and $C(14, 0, -2)$ 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 $\frac{2m}{n} - \frac{a}{3} =$