What engine do you have in the Vitara - a 2003 could be a 1.6 or a 2.0?
Does the engine shut off - or - does it stall - which is it?
These are actually two different symptoms which point to different causes - if you hold the throttle open - to say 1500 rpm (or if you're driving) and you switch on the a/c - what happens?
Does the engine die? You probably have an electrical issue.
Does the engine continue to run? I would suspect the IAC (idle air control)motor, although there are other possiblities.
Switching on the a/c increases the load on the engine from two sources - there is a/c compressor load, and increased electrical load from the evaporator & condensor fans - the increased load cause the idle rpm to decrease and the ECU compensates by allowing more air flow through the idle air control - if this fails it may not set a code.