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:

$A$ point moves in such a way that the sum of its distances from the $xy$-plane and $yz$-plane remains equal to its distance from the $zx$-plane. The locus of the point is:

Are the points $A(3, 6, 9)$,$B(10, 20, 30)$,and $C(25, -41, 5)$ the vertices of a right-angled triangle?

If the points $(-1, 3, 2)$,$(-4, 2, -2)$,and $(5, 5, \lambda)$ are collinear,then $\lambda = $

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

If the vertices of a triangle $ABC$ are $A(1, 2, 3)$,$B(h, -3, 0)$,and $C(-4, k, -1)$ and the centroid of the triangle is $\left(5, -1, \frac{2}{3}\right)$,then triangle $ABC$ is