The incentre of the triangle $ABC$,whose vertices are $A(0,2,1)$,$B(-2,0,0)$ and $C(-2,0,2)$,is

Assertion $(A):$ If $(-1,3,2)$ and $(5,3,2)$ are respectively the orthocentre and circumcentre of a triangle, then $(3,3,2)$ is its centroid.
Reason $(R):$ Centroid of the triangle divides the line segment joining the orthocentre and the circumcentre in the ratio $1: 2$.
Which one of the following is true?

Let $A=(1,2,0)$, $B=(2,0,-1)$, $C=(0,-2,3)$ and $D=(-1,2,-3)$ be four points in space. Let $G_1$ be the centroid of triangle $ABC$ and $G_2$ be the centroid of tetrahedron $ABCD$. If $P$ divides $G_1G_2$ in the ratio $4:3$ internally, then $P=$

Tetrahedron $ABCD$ has side lengths $AB = CD = 12$. These edges are perpendicular to each other. Let $E$ and $F$ be the midpoints of $AB$ and $CD$ respectively. Given that $EF = 10$ and $EF$ is perpendicular to both $AB$ and $CD$,find the volume of the tetrahedron $ABCD$.

The incentre of the triangle whose vertices are $P(0,3,0)$,$Q(0,0,4)$,and $R(0,3,4)$ is

Find the length of the perpendicular drawn from the point $P(2\hat{i} - \hat{j} + 5\hat{k})$ to the line $\vec{r} = (11\hat{i} - 2\hat{j} - 8\hat{k}) + \lambda(10\hat{i} - 4\hat{j} - 11\hat{k})$.