The centroid of a triangle $ABC$ is at the point $(1,1,1)$. If the coordinates of $A$ and $B$ are $(3,-5,7)$ and $(-1,7,-6)$ respectively,find the coordinates of the point $C$.

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 $\qquad$ .

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

If $P(3,2,6), Q(1,4,5)$ and $R(3,5,3)$ are the vertices of $\Delta PQR$,then $m \angle PQR$ is (in $^{\circ}$)

If the midpoints of the sides $AB$, $BC$, and $CA$ of a triangle are respectively $D(1, 2, -3)$, $E(3, 0, 1)$, and $F(-1, 1, -4)$, then the centroid of the triangle $ADF$ is