If the orthocentre and the centroid of a triangle are $(-3,5,2)$ and $(3,3,4)$ respectively,then its circumcentre is

$AB$ and $BC$ are diagonals of adjacent faces of a rectangular box with its center at the origin,and its edges parallel to the coordinate axes. If the angles $\angle BOC, \angle COA$,and $\angle AOB$ are $\alpha, \beta$,and $\gamma$ respectively,then $\cos \alpha + \cos \beta + \cos \gamma$ is equal to:

Find the equation of the set of points $P$,the sum of whose distances from $A(4, 0, 0)$ and $B(-4, 0, 0)$ is equal to $10$.

Three identical balls of radius $2 \, cm$ each are placed on a table such that they touch each other as well as the table. Now a fourth ball of the same radius is placed above these three balls. The height of the highest point on the fourth ball above the table is -

Let $A(1, 8, 4)$, $B(0, -11, 3)$, and $C(2, -3, -1)$ be three points. If $D$ is the foot of the perpendicular from $A$ to the line $BC$, find the coordinates of $D$.

Find the reflection of the point $(1, 6, 3)$ in the line $\frac{x}{1} = \frac{y - 1}{2} = \frac{z - 2}{3}$.