As I understand, in Java, stack memory holds primitives and method invocations and heap memory is used to store objects.

Suppose I have a class

class A {
       int a ;
       String b;
       //getters and setters
}

1. Where will the primitive a in class A be stored?

2. Why does heap memory exist at all? Why can't we store everything on the stack?

3. When the object gets garbage collected, is the stack associated with the objected destroyed?