Minimum distance between two satellites

A space base has traced stallites A and B at a particular moment at:
A0 = (a1,0,a3) B0 = (0,b2,b3)
whereas the base itself is located at the origin (0,0,0) and the satellites move at constant velocities with respect to the base:
Va = (Va,0,0) Vb = (Vb,Vb,0)

The minimum distance between satellites A and B ought to be computed.

My proposed solution:

OA = A0 + Va * t = (a1,0,a3) + (Va,0,0)t
OB = B0 + Vb * t = (0,b2,b3) + (Vb,Vb,0)t

I found the minimum distance to be:

SQRT[1/2(a1+b2)^2 + (b3-a3)^2]

Am I correct? Could someone please confirm?