If the origin is the centroid of the triangle $PQR$ with vertices $P(2a, 2, 6)$,$Q(-4, 3b, -10)$,and $R(8, 14, 2c)$,then the values of $a, b, c$ respectively are:

Let $A(4, -2)$,$B(1, 1)$,and $C(9, -3)$ be the vertices of a triangle $ABC$. Then the maximum area of the parallelogram $AFDE$,formed with vertices $D, E$,and $F$ on the sides $BC, CA$,and $AB$ of the triangle $ABC$ respectively,is $\qquad$ .

Which of the following statements are true?

If $D(2, 1, 0)$, $E(2, 0, 0)$, and $F(0, 1, 0)$ are the mid-points of the sides $BC$, $CA$, and $AB$ of $\triangle ABC$, respectively, then the centroid of $\triangle ABC$ is:

Let $A(x, y, z)$ be a point in the $xy$-plane,which is equidistant from three points $P(0, 3, 2)$,$Q(2, 0, 3)$,and $R(0, 0, 1)$. Let $B = (1, 4, -1)$ and $C = (2, 0, -2)$. Then among the statements $(S1) :$ $\triangle ABC$ is an isosceles right-angled triangle and $(S2) :$ the area of $\triangle ABC$ is $\frac{9 \sqrt{2}}{2}$.

$A(2,3,-4), B(-3,3,-2), C(-1,4,2), D(3,5,1)$ are the vertices of a tetrahedron. If $G_1, G_2$ and $G_3$ are the centroids of the three faces having the vertex $D$ in common,then the centroid of the $\Delta G_1 G_2 G_3$ is