Find the centroid of a triangle,the mid-points of whose sides are $D(1, 2, -3)$,$E(3, 0, 1)$,and $F(-1, 1, -4)$.

If $G(4, 3, 3)$ is the centroid of the triangle $ABC$ whose vertices are $A(a, 3, 1)$,$B(4, 5, b)$,and $C(6, c, 5)$,then the values of $a, b, c$ are:

If the mid-points of the sides $AB, BC, CA$ of a triangle are $(1, 5, -1), (0, 4, -2), (2, 3, 4)$ respectively,then the length of the median drawn from $C$ to $AB$ is

Let $ABCD$ be a tetrahedron in which the coordinates of each of its vertices are in arithmetic progression. If the centroid $G$ of the tetrahedron is $(2, 3, k)$,then the distance of $G$ from the origin is

If the points $A(0, 1, 2)$,$B(2, -1, 3)$,and $C(1, -3, 1)$ are the vertices of a triangle,then the triangle is

In $\triangle ABC$,if the midpoints of the sides $AB, BC$ and $CA$ are respectively $(l, 0, 0), (0, m, 0)$ and $(0, 0, n)$,then $\frac{AB^2+BC^2+CA^2}{l^2+m^2+n^2}=$