The relaxation is supposed to provide you with the structure different from the initial one. Therefore, strictly speeking, you should not be surprised if you get different b/a and/or c/a. Perhaps, your intention was to relax positions while keeping the cell the same. Then you have to choose the proper option - there is a variety of them. However, since your relaxation leads to completely different structure I would look also to other options - like correct POTCAR (elements in the proper sequence and atoms in the proper sequence, number of k-Points, cut-off etc etc etc - there are quite a few ways to get it wrong and comparbaly few to get it right). I also suggest to register on the VASP forim where you will find a higher concentration of VASP experts in comparison to this forum.
If you want to keep your lattice fixed you can do a relaxation using ISIF=2. Than only the atoms will be moved, yet the lattice vectors remain constant (I am not sure if this is really what you want to do). However, if you use e.g. ISIF=3 atoms and lattice parameters will be relaxed.