strange behaviour when vector elemnts are set using indexing

Trying to copy all elements from one vector to another using indexing as shown in code snippet. As far as I understand, setting/getting an element in vector using index(I'm aware about "at" and its benefits) is allowed in C++.

If I set an element in vector a using index, it works as expected. For vector b also, If push_back is used, it works as expected.

int main() 
{   
vector<int> a{1,3,6,10,56,9};
vector<int> b;
b.reserve(a.size());
cout << "1. a[2]: " << a[2] << endl;
a[2] = 100;
cout << "2. a[2]: " << a[2] << endl;
for(int i=0; i<a.size(); ++i)
{
    b[i] = a[i];
}
cout << "1. b.size() : " << b.size() << endl;


for(int i=0; i<a.size(); ++i)
{
    b.push_back(a[i]);
}
cout << "2. b.size() : " << b.size() << endl;
return 0;
}

I'm finding it difficult to understand this behaviour of vector.

Note: I know this is not a suggested way of copying vector as we have multiple other options which both convenient and effective.

output:

1. a[2]: 6
2. a[2]: 100
1. b.size() : 0
2. b.size() : 6