If the centroid of a triangle with vertices $(4, p, -3)$,$(-1, -1, 2)$,and $(3, 5, -8)$ is given by the mid-point of $(1, 4, -2)$ and $(q, 2, -4)$,then $p^2 + q^2 =$

Let the centroid of a triangle formed by the points $A(4, x, 1)$,$B(y, -5, 2)$ and $C(7, 8, 3)$ be $G(3, 5, 2)$ and $CG$ meet $AB$ in $F$. Then,$F=$

$A(3, 2, -1), B(4, 1, 1), C(6, 2, 5)$ are three points. If $D, E, F$ are three points which divide $BC, CA, AB$ respectively in the same ratio $2: 1$,then the centroid of $\triangle DEF$ is

The mid-points of the sides of a triangle are $(5,7,11)$,$(0,8,5)$,and $(2,3,-1)$. Find its vertices.

If the origin is the centroid of the triangle whose vertices are $A(2, p, -3)$,$B(q, -2, 5)$,and $C(-5, 1, r)$,then

Let $A (2, 3, 5)$,$B (-1, 3, 2)$ and $C (\lambda, 5, \mu)$ be the vertices of a $\Delta ABC$. If the median through $A$ is equally inclined to the coordinate axes,then