Perpendicular to RA and DEC direction

[Philosophaie]

I would like to know how to find a acceleration perpendicular to the center of mass for an object traveling in a RA and DEC direction at an arbitrary angle away from the perpendicular to an object. I want to know this to be able to produce a Roll with a constant vectoring of the engines to produce this perpendicular acceleration.

 

[Poscik]

Cross product of these two vectors.

 

[Philosophaie]

(ax,ay,az)X(arx,ary,arz) = 0
where a is the original acceleration and ar is the introduced roll acceleration perpendicular to vector (ax,ay,ay). Find ar.

Introducing vector ap = (apx,apy,apz). It is also perpendicular to a.

How do I tell if it us on the same plane as ar?