Let $(3, 4, -1)$ and $(-1, 2, 3)$ be the end points of a diameter of a sphere. Then the radius of the sphere is equal to

The coordinate of a point equidistant from the points $(0, 0, 0), (a, 0, 0), (0, b, 0),$ and $(0, 0, c)$ is

$A$ 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

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?

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

The locus of the equation ${x^2} + {y^2} + {z^2} + 1 = 0$ is