If $A(-4, 5, p)$,$B(3, 1, 4)$,and $C(-2, 0, q)$ are the vertices of a triangle $ABC$ and $G(r, q, 1)$ is its centroid,then the value of $2p + q - r$ is equal to

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 centroid of a triangle with vertices $(4, p, -3)$,$(-1, -1, 2)$,and $(3, 5, -8)$ is given by the mid-point of $(1, 4, -2)$ and $(q, 2, -4)$,then $p^2 + q^2 =$

$A(3, 2, -1), B(4, 1, 1), C(6, 2, 5)$ are three points. If $D, E, F$ are three points which divide $BC, CA, AB$ respectively in the same ratio $2: 1$,then the centroid of $\triangle DEF$ is

If the points $A(1, 3, 5)$, $B(2, 4, 6)$, and $C(4, 5, k)$ form a right-angled triangle, then the number of possible values of $k$ is:

The points $(-2, 4, 7)$,$(3, -6, -8)$,and $(1, -2, -2)$ are: