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:

$A$ spherical ball is kept at the corner of a rectangular room such that the ball touches two perpendicular walls and lies on the floor. If a point on the sphere is at distances of $9, 16, 25$ from the two walls and the floor,then a possible radius of the sphere is

The intersection of the spheres ${x^2} + {y^2} + {z^2} + 7x - 2y - z = 13$ and ${x^2} + {y^2} + {z^2} - 3x + 3y + 4z = 8$ is the same as the intersection of one of the spheres and the plane:

The equation ${x^2} + {y^2} + {z^2} = 0$ represents

$A$ 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:

The centre of the sphere $\alpha \,r^2 - 2u \cdot r = \beta ,(\alpha \ne 0)$ is