What is a good ratio between Life, Armor and Resistances?
There is an equally simple answer for Armor vs Resistances - you should also keep them at 10:1. One point of Resistance provides exactly the same benefit as ten points of Armor.
Formulas:
- Damage Resistance from Armor = Armor / (50*Level + Armor)
- Damage Resistance from Resistances = Resist / (5*Level + Resist)
Assuming attacker level to be 70, and combining both formulas together multiplicatively (as they are in the game) we can define Relative Toughness as the relation of Toughness (Effective Hit Points) to naked, no-mitigation Life.
- Relative Toughness = (1 + (A / 3500)) * (1 + (R / 350))
In simple terms, each 35 Armor and each 3,5 Resistance make you 1% tougher. These are multiplied together, thus:
Armor Resistance Relative Toughness
0 0 100%
7000 0 300%
0 700 300%
3500 350 400%
Concerning Life vs Mitigation there are two things to consider.
First, you need to maximize your Toughness. For this, ideal ratio would be "50% mitigation for each 500 Vitality over 1000", but this formula is practically useless, because your mitigation is going to rise at at least quadratic rate (from Armor multiplied by Resistance), and your Life will also depend on both Vitality and +% Life.
Practical advice about maximizing Toughness is simply "use item tooltips". For high-risk cases, like crafting and cubing, it is better to go the long way, comparing the complete formula for both cases.
And the most complex case is Recovery. Best survivability is not achieved by Toughness, but rather by just enough Toughness to not be one-shot, and plenty of Recovery to survive indefinitely without having to rely on potions. There is no hard rule on Recovery, but Diablo's gradual difficulty increase allows to judge for yourself - as soon as you start to rely on Potions and run in circles, you need more Recovery.
And Recovery benefits from lower Life and higher mitigation, so above mentioned "50% DR to 500 Vitality" goes out of the window :-)