What you are trying to achive is not possible. The difference is that you are creating a class A and then creating an array with 10 elements of A while vector is a class that represents the array itself.
Just compare it to an int array:
Code:
int x[10];
for(int i=0; i < x.size; i++)
Since the native C array does not store the size unlike in Java, in your argumentation you wouls have to add it to int as you are trying to add it to A.
See? If you want to understand vector (which is basically not that complicated.. It's just Microsoft's standard headers that seem a bit complicated to beginners), you have to write your own class that stores other elements. You just created a simple class and made an array of it; how should the elements know about the array size? And the array itself cannot know it, because it's a C style array and C does not know classes.
Btw. for arrays you can use the ARRAYSIZE macro or the C++ class std::array.