The points $(2, 3, 4)$,$(-1, -2, 1)$,and $(5, 8, 7)$ are

If the circumcenter of the triangle formed by the points $(1,2,3), (3,-1,5)$ and $(4,0,-3)$ is $(\alpha, \beta, \gamma)$, then $|\alpha|+|\beta|=$

If $(1,0,3), (2,1,5), (-2,3,6)$ are the mid-points of the sides of a triangle, then the centroid of the triangle is

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

In a triangle $ABC$, if the midpoints of sides $AB, BC, CA$ are $(3,0,0), (0,4,0), (0,0,5)$ respectively, then $AB^2+BC^2+CA^2=$

$\triangle ABC$ has vertices at $A \equiv (2, 3, 5)$,$B \equiv (-1, 3, 2)$ and $C \equiv (\lambda, 5, \mu)$. If the median through $A$ is equally inclined to the axes,then the values of $\lambda$ and $\mu$ respectively are