If the origin is the centroid of the triangle whose vertices are $A(2, p, -3)$,$B(q, -2, 5)$,and $C(-5, 1, r)$,then

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 perimeter of the triangle with vertices at $(1,0,0), (0,1,0)$ and $(0,0,1)$ 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

Three consecutive vertices of a parallelogram $ABCD$ are $A(6, -2, 4)$,$B(2, 4, -8)$,and $C(-2, 2, 4)$. Find the coordinates of the fourth vertex $D$.

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 $\qquad$ .