Ok let's say that I have the exploit arcane weapon and used in the spell Instant weapon that it let me create a Melee weapon and be proficiency in that weapon, now I have a doubt can arcane weapon exploit can be applied to mage sword spell?
can arcane weapon exploit can be applied to mage sword spell?
Maybe not every spell, but instant weapon “acts in all ways as a masterwork weapon typical of its type”, so there is no reason it shouldn’t work.
This spell brings into being a shimmering, sword-like plane of force. The sword strikes at any opponent within its range, as you desire, starting in the round that you cast the spell. The sword attacks its designated target once each round on your turn. Its attack bonus is equal to your caster level + your Intelligence bonus or your Charisma bonus (for wizards or sorcerers, respectively) with an additional +3 enhancement bonus. As a force effect, it can strike ethereal and incorporeal creatures. It deals 4d6+3 points of force damage, with a threat range of 19–20 and a critical multiplier of ×2
Arcane weapon only works for weapons the arcanist is actually wielding. The wording of Mage’s Sword states the sword attacks, not that the caster wields the sword. So, Arcane Weapon does not work with Mage’s Sword. It is also not an actual sword so that also means it does not work.