If $A(0,4,0)$,$B(0,0,3)$,and $C(0,4,3)$ are the vertices of $\Delta ABC$,then its incentre is

Find the centroid of a triangle,the mid-points of whose sides are $D(1, 2, -3)$,$E(3, 0, 1)$,and $F(-1, 1, -4)$.

If the centroid of $\Delta ABC$ is $(0,0,0)$,where $A(1,1,1), B(2,1,2), C(x, y, z)$,then $(x, y, z) = \ldots \ldots$

$A$ parallelogram has vertices $A(4,4,-1)$,$B(5,6,-1)$,$C(6,5,1)$ and $D(x, y, z)$. Then the vertex $D$ is

Let $A(x, y, z)$ be a point in the $xy$-plane,which is equidistant from three points $P(0, 3, 2)$,$Q(2, 0, 3)$,and $R(0, 0, 1)$. Let $B = (1, 4, -1)$ and $C = (2, 0, -2)$. Then among the statements $(S1) :$ $\triangle ABC$ is an isosceles right-angled triangle and $(S2) :$ the area of $\triangle ABC$ is $\frac{9 \sqrt{2}}{2}$.

Find the lengths of the medians of the triangle with vertices $A(0,0,6)$,$B(0,4,0)$,and $C(6,0,0)$.