If $(2, 3, 5)$ is one end of a diameter of the sphere ${x^2} + {y^2} + {z^2} - 6x - 12y - 2z + 20 = 0$,then the coordinates of the other end of the diameter are:

If $A$ and $B$ are the points $(3, 4, 5)$ and $(-1, 3, -7)$ respectively,find the equation of the set of points $P$ such that $PA^{2} + PB^{2} = k^{2}$,where $k$ is a constant.

How many distinct spheres of radius $r$ can be drawn such that they touch all three coordinate planes?

$A$ variable plane passes through a fixed point $P(1, 2, 3)$. The foot of the perpendicular from the origin $O(0, 0, 0)$ to the plane lies on:

If $r$ is the position vector of any point on a sphere and $a$ and $b$ are the position vectors of the extremities of a diameter,then which of the following is true?

If the plane $2ax - 3ay + 4az + 6 = 0$ passes through the midpoint of the line segment joining the centers of the spheres $x^2 + y^2 + z^2 + 6x - 8y - 2z = 13$ and $x^2 + y^2 + z^2 - 10x + 4y - 2z = 8$,then $a = ......$