The midpoints of the sides of a triangle are $(1, 5, -1)$,$(0, 4, -2)$,and $(2, 3, 4)$. Find the centroid of the triangle.

If two vertices of a triangle are $A(3,1,4)$ and $B(-4,5,-3)$ and the centroid of the triangle is $G(-1,2,1)$,then the third vertex $C$ of the triangle is

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 find the values of $a, b$,and $c$.

If the centroid of the triangle whose vertices are $(a, 1, 3)$,$(-2, b, -5)$,and $(4, 7, c)$ is the origin,then $a^2 + b^2 + c^2 =$

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 points $A(0, 1, 2)$,$B(2, -1, 3)$,and $C(1, -3, 1)$ are the vertices of a triangle,then the triangle is