If the origin is the centroid of the triangle for which $(-2, 3, 4)$ and $(3, -1, 5)$ are two vertices,then the third vertex is

The incenter and centroid of the triangle,whose vertices are $A \equiv(0,3,0), B \equiv(0,0,4)$,and $C \equiv(0,3,4)$,are respectively given by

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 $\qquad$ .

If the points $(2,4,-1), (3,6,-1)$ and $(4,5,1)$ are three consecutive vertices of a parallelogram,then its fourth vertex is

If $O(0,0,0), A(3,0,0), B(0,4,0)$ form a triangle,then the incentre of triangle $OAB$ is

If the origin is the centroid of a triangle $ABC$ having vertices $A(a, 1, 3)$,$B(-2, b, -5)$,and $C(4, 7, c)$,find the values of $a, b, c$.