Which method is used to add an element to a vector in C++?

The method used to add an element to a vector in C++ is the push_back() function. This member function specifically appends a new element to the end of the vector, effectively increasing its size by one. The advantage of push_back() is that it automatically takes care of memory allocation and resizing the vector as needed when new elements are added.

The other options, while they may seem intuitive, do not correspond to C++ standard library vector operations. For example, add() and append() are not existing functions in the vector class; hence, trying to use them would result in a compilation error. The insert() function does allow for adding elements but does so at a specified position rather than solely at the end. Therefore, for simply adding an element to the back of a vector, push_back() is the most straightforward and appropriate method.