If the centroid of $\Delta ABC$ is $(0,0,0)$,where $A(1,1,1), B(2,1,2), C(x, y, z)$,then $(x, y, z) = \ldots \ldots$

The centroid of a tetrahedron with vertices $A(3, -5, x)$,$B(5, 4, 2)$,$C(7, -7, y)$,and $D(1, 0, z)$ is $G(4, -2, 2)$. Then,the value of $x + y + z$ is:

If $A(1,4,2)$ and $C(5,-7,1)$ are two vertices of triangle $ABC$ and $G\left(\frac{4}{3}, 0, \frac{-2}{3}\right)$ is the centroid of the triangle $ABC$,then the midpoint of side $BC$ is

Let $ABCD$ be a parallelogram and $E$ be the mid-point of $AB$. If $P$ is the point of intersection of $DE$ and $AC$,then $\frac{DP}{PE} + \frac{AP}{PC} = $

Consider a cuboid where all edges are integers and the base is a square. Suppose the sum of all its edges is numerically equal to the sum of the areas of all its six faces. Then,the sum of all its edges is

Which of the following statements are true?