My file fails to compile due to `insert` and `find` functions of `vector`

Question

I am a beginner in C++ language. When I try to compile a file with g++ I get the following error. I'm pretty sure the errors are all on find and insert. I went online to try and get help, but a lot of people say just #include <algorithm> will do. I did do that, but it still doesn't compile. Below is my code and error message.

Intersection of Two Arrays.cpp:11:22: error: ‘class std::vector<int>’ has no member named ‘find’
   11 |         if (nums_set.find(num) != nums_set.end()) {
      |                      ^~~~
Intersection of Two Arrays.cpp:12:34: error: no matching function for call to ‘std::vector<int>::insert(int&)’
   12 |             result_set.insert(num);
      |                                  ^
In file included from /usr/include/c++/9/vector:72,
                 from Intersection of Two Arrays.cpp:2:
/usr/include/c++/9/bits/vector.tcc:130:5: note: candidate: ‘std::vector<_Tp, _Alloc>::iterator std::vector<_Tp, _Alloc>::insert(std::vector<_Tp, _Alloc>::const_iterator, const value_type&) [with _Tp = int; _Alloc = std::allocator<int>; std::vector<_Tp, _Alloc>::iterator = __gnu_cxx::__normal_iterator<int*, std::vector<int> >; typename std::_Vector_base<_Tp, _Alloc>::pointer = int*; std::vector<_Tp, _Alloc>::const_iterator = __gnu_cxx::__normal_iterator<const int*, std::vector<int> >; typename __gnu_cxx::__alloc_traits<typename std::_Vector_base<_Tp, _Alloc>::_Tp_alloc_type>::const_pointer = const int*; std::vector<_Tp, _Alloc>::value_type = int]’
  130 |     vector<_Tp, _Alloc>::
      |     ^~~~~~~~~~~~~~~~~~~
/usr/include/c++/9/bits/vector.tcc:130:5: note:   candidate expects 2 arguments, 1 provided
In file included from /usr/include/c++/9/vector:67,
                 from Intersection of Two Arrays.cpp:2:
/usr/include/c++/9/bits/stl_vector.h:1290:7: note: candidate: ‘std::vector<_Tp, _Alloc>::iterator std::vector<_Tp, _Alloc>::insert(std::vector<_Tp, _Alloc>::const_iterator, std::vector<_Tp, _Alloc>::value_type&&) [with _Tp = int; _Alloc = std::allocator<int>; std::vector<_Tp, _Alloc>::iterator = __gnu_cxx::__normal_iterator<int*, std::vector<int> >; typename std::_Vector_base<_Tp, _Alloc>::pointer = int*; std::vector<_Tp, _Alloc>::const_iterator = __gnu_cxx::__normal_iterator<const int*, std::vector<int> >; typename __gnu_cxx::__alloc_traits<typename std::_Vector_base<_Tp, _Alloc>::_Tp_alloc_type>::const_pointer = const int*; std::vector<_Tp, _Alloc>::value_type = int]’
 1290 |       insert(const_iterator __position, value_type&& __x)
      |       ^~~~~~
/usr/include/c++/9/bits/stl_vector.h:1290:7: note:   candidate expects 2 arguments, 1 provided
/usr/include/c++/9/bits/stl_vector.h:1307:7: note: candidate: ‘std::vector<_Tp, _Alloc>::iterator std::vector<_Tp, _Alloc>::insert(std::vector<_Tp, _Alloc>::const_iterator, std::initializer_list<_Tp>) [with _Tp = int; _Alloc = std::allocator<int>; std::vector<_Tp, _Alloc>::iterator = __gnu_cxx::__normal_iterator<int*, std::vector<int> >; typename std::_Vector_base<_Tp, _Alloc>::pointer = int*; std::vector<_Tp, _Alloc>::const_iterator = __gnu_cxx::__normal_iterator<const int*, std::vector<int> >; typename __gnu_cxx::__alloc_traits<typename std::_Vector_base<_Tp, _Alloc>::_Tp_alloc_type>::const_pointer = const int*]’
 1307 |       insert(const_iterator __position, initializer_list<value_type> __l)
      |       ^~~~~~
/usr/include/c++/9/bits/stl_vector.h:1307:7: note:   candidate expects 2 arguments, 1 provided
/usr/include/c++/9/bits/stl_vector.h:1332:7: note: candidate: ‘std::vector<_Tp, _Alloc>::iterator std::vector<_Tp, _Alloc>::insert(std::vector<_Tp, _Alloc>::const_iterator, std::vector<_Tp, _Alloc>::size_type, const value_type&) [with _Tp = int; _Alloc = std::allocator<int>; std::vector<_Tp, _Alloc>::iterator = __gnu_cxx::__normal_iterator<int*, std::vector<int> >; typename std::_Vector_base<_Tp, _Alloc>::pointer = int*; std::vector<_Tp, _Alloc>::const_iterator = __gnu_cxx::__normal_iterator<const int*, std::vector<int> >; typename __gnu_cxx::__alloc_traits<typename std::_Vector_base<_Tp, _Alloc>::_Tp_alloc_type>::const_pointer = const int*; std::vector<_Tp, _Alloc>::size_type = long unsigned int; std::vector<_Tp, _Alloc>::value_type = int]’
 1332 |       insert(const_iterator __position, size_type __n, const value_type& __x)
      |       ^~~~~~
/usr/include/c++/9/bits/stl_vector.h:1332:7: note:   candidate expects 3 arguments, 1 provided
/usr/include/c++/9/bits/stl_vector.h:1376:2: note: candidate: ‘template<class _InputIterator, class> std::vector<_Tp, _Alloc>::iterator std::vector<_Tp, _Alloc>::insert(std::vector<_Tp, _Alloc>::const_iterator, _InputIterator, _InputIterator) [with _InputIterator = _InputIterator; <template-parameter-2-2> = <template-parameter-1-2>; _Tp = int; _Alloc = std::allocator<int>]’
 1376 |  insert(const_iterator __position, _InputIterator __first,
      |  ^~~~~~
/usr/include/c++/9/bits/stl_vector.h:1376:2: note:   template argument deduction/substitution failed:
Intersection of Two Arrays.cpp:12:34: note:   candidate expects 3 arguments, 1 provided
   12 |             result_set.insert(num);
      |                                  ^

#include <iostream>
#include <vector>
#include <algorithm>

using namespace std;

vector<int> intersection(vector<int>& nums1, vector<int>& nums2) {
    vector<int> result_set;
    vector<int> nums_set(nums1.begin(), nums1.end());
    for (int num : nums2) {
        if (nums_set.find(num) != nums_set.end()) {
            result_set.insert(num);
        }
    }
    return vector<int>(result_set.begin(), result_set.end());
}

Note: The main function of this equation is to return the elements contained in both vectors.