Mirage IIIEA were not capable to hunt the Avro Vulcan due to several reasons.
The first one is the range without air refueling, those airplanes were limited to 10 min at station over Malvinas flying higher than FL260.
So when the Argentine's long range radars were detecting the bomber at around 150 NM from Puerto Argentino, the MIIIEA have to be scramble from Rio Gallegos at not less than 40 min flight time...no chance at all to get an interception.
On June 10th, the Argentine Air Force Boeing B707-320 flying long range recce detecting three airplanes flying to Malvinas.
Those airplanes were presumed as Avro Vulcan or Nimrod, so a mission of four MIIIEA were lunched for hunting them but they couldn't get any contact when arrived to the target area.