As for partial tear, you may need to consult with your doctor regarding with that problem but I will say that overuse is usually the cause of a torn quad. Eccentric force puts lots of stress on the muscle and tight hips and quads can lead to muscle imbalances.
Running down hill, landing from a jump or simply just lowering your body on one leg abruptly can lead to a tear. However, everyone’s situation is unique and it takes a lot of weakening of the muscles for this to occur. Lastly, for a tear to occur, it takes lot of abuse to the muscle. I hope that helps clear things up.