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

$A$ 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 radius of the circle formed by the intersection of the plane $x + 2y + 2z = 15$ and the sphere ${x^2} + {y^2} + {z^2} - 2y - 4z = 11$ 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?

$A$ plane passes through a fixed point $(p, q, r)$ and cuts the axes at $A, B, C$. Then the locus of the centre of the sphere $OABC$ is

If the volume of a sphere increases by $72.8 \%$,then its surface area increases by $... \%$