Friend function can't access class variables and can't understand Namespaces - c++

Question

I thought that friend functions could access class variables as in how I try to do v.x, v.y, v.z in the << function. But it doesn't compile. It says it's unable to resolve identifier at those lines.
Also I'm trying to learn how to use namespaces. Even though I use the namespace vec in the implementation file I still have to include Vector:: before everything so what's the point?
Header file:
#ifndef VECTOR_H
#define VECTOR_H
namespace vec {
class Vector {
private:
double x, y, z;
public:
Vector(double, double, double);
friend std::ostream& operator<<(std::ostream&, const Vector&);
};
}
#endif /* VECTOR_H */
.cpp file:
#include "Vector.h"
#include <iostream>
using namespace vec;
//Constructor
Vector::Vector(double x1 = 0, double y1 = 0, double z1 = 0) {
x = x1;
y = y1;
z = z1;
}
//Have also tried adding vec:: and Vector:: before operator<< here.
std::ostream& operator<<(std::ostream& out, const Vector& v) {
out<<"<"<<v.x<<", "<<v.y<<", "<<v.z<<">";
return out;
}

Answer 1

I believe part of the problem is that your vec.h doesn't have #include <iostream>, so the type std::ostream is unidentified in that file, and since that part is compiled before the vec.cpp main part, it fails to recognise your function.
You also need to put your operator<< into the namespace of vec. After all, you have asked for a friend function within that namespace.
With these two changes, your code compiles with gcc -Wall -Wextra -O2.

Answer 2

Your compile error may relative to below issues:
Default parameter only goes to function declaration not function
definition, you are doing the other way around.
Also, in Vector.cpp you should wrap up your class member function
definitions in namespace instead of calling using directive.
Try:
Vector.h
#include <iostream>
class Vector {
private:
double x, y, z;
public:
Vector(double x1 = 0, double y1 = 0, double z1 = 0);
^^ ^^ ^^
friend std::ostream& operator<<(std::ostream&, const Vector&);
};
Vector.cpp
namespace vec
{
Vector::Vector(double x1, double y1, double z1)
:x(x1), y(y1), z(z1)
{
}
}

Answer 3

The friend std::ostream& operator<< declaration appears in namespace vec, so the definition should be prefixed by vec::. Your comment says you tried that - maybe you got confused by the other error messages billz documents, but you should reinstate vec::operator<< or surround it with namespace vec { ... }.
This creates an error like:
ns.cc: In function `int main()':
ns.cc:26: error: ambiguous overload for 'operator<<' in 'std::cout << w'
ns.cc:19: note: candidates are: std::ostream& operator<<(std::ostream&, const vec::Vec&)
ns.cc:10: note: std::ostream& vec::operator<<(std::ostream&, const vec::Vec&)