I am trying to rotate a point say (20,6,30) around a point (10,6,10) at a radius of 2

The above requirement can be fulfilled if the axis of rotation passes through (10,6,10) and passes through a point that is 2 length units away from (20,6,30).

Think of the rotational axis as a ray emanating at the center of rotation **r**_{0} (here (10,6,10)) along a direction **d**:

**r**( t ) := **r**_{0} + t * **d**

The second point is at a distance t_{1} on this ray. The difference vector **v** from here to the point of interest **p** (here (20,6,30)) is:

**p** - **r**( t_{1} ) =: **v**

It is constrained because it is perpendicular to **d**

**v** x **d** == 0

and its length should be 2

|| **v** || == 2

Try to solve this, but you'll see that there is an infinite amount of solutions to this. ~~Think of a circle with radius 2 around ~~ EDIT: Ups, the figure isn't necessarily a circle, sorry. But it still may help as a gedanken experiment if thinking of a circle.**p**, and the 2nd point **r**( t_{1} ) on the ray may be any point of this circle. Whatever point you choose will have an influence on how the rotation looks like.