Damage Reduction and Vile Damage

[Yogibear41]

If a person with a damage reduction of say 10/- is attacked by someone with a greatsword who has the vile martial strike feat and the attack results in 10 damage from the sword and 1 point of vile damage from the feat does 1 point of normal damage go through or 1 point of vile damage?

[Crake]

If a person with a damage reduction of say 10/- is attacked by someone with a greatsword who has the vile martial strike feat and the attack results in 10 damage from the sword and 1 point of vile damage from the feat does 1 point of normal damage go through or 1 point of vile damage?

No damage happens. This is because the vile martial strike feat does not increase your damage dealt, but rather does a point of vile damage each time you deal weapon damage. Since your initial 10 damage didn't make it past the DR of the creature, the vile damage never occurs. It is worth noting that they are treated as separate damage "packets", and that vile damage is not affected by DR, similar to how a flaming weapon doesn't increase the damage you deal on your attack, but rather does a separate packet of 1d6 fire damage. Note however that a flaming weapon only requires a hit, not that you deal damage, so if you did 7 points of damage vs the DR10/- your flaming weapon would still deal 1d6 fire damage regardless (though potentially blocked by any fire resistance the creature might have).

In summary:

Vile damage is not affected by DR
The vile damage from Vile Martial Strike is a separate packet of damage
Vile Martial Strike only does an extra point of vile damage if the initial attack dealt damage itself