The length of the altitude through the point $D$ of a tetrahedron with vertices $A(2,3,1)$,$B(4,1,-2)$,$C(6,3,7)$,and $D(-5,-4,8)$ is: (in $units$)

$A$ tetrahedron of volume $5$ has three of its vertices at the points $A(2,1,-1)$,$B(3,0,1)$,and $C(2,-1,3)$. If the fourth vertex $D$ lies on the $y$-axis,then the sum of the ordinates of all possible points $D$ is-

Find the point in the $XY$-plane which is equidistant from the three points $A(2, 0, 3)$,$B(0, 3, 2)$,and $C(0, 0, 1)$.

If the vertices of $\Delta ABC$ are $(a, 0, 0)$,$(0, b, 0)$,and $(0, 0, c)$ respectively,then $\angle B = \dots$

Find the reflection of the point $P(2, -1, 3)$ in the plane $3x - 2y - z = 9$.

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?