友元函数却不能访问私有成员，是怎么回事？

#ifndef VECTOR_H_
#define VECTOR_H_
#include <iostream>
using namespace std;

class Vector
{
private:
    double x;
    double y;
    double mag;
    double ang;
    char mode;
    //private methods
    void set_mag();
    void set_ang();
    void set_x();
    void set_y();

public:
    Vector();
    Vector(double n1, double n2, char form='r');
    void set(double n1, double n2, char form='r');
    ~Vector();
    double xval() const { return x; }
    double yval() const { return y; }
    double magval() const { return mag; }
    double angval() const { return ang; }
    void polar_mode();
    void rect_mode();
    //operator overloading
    Vector operator+(const Vector &v) const;
    Vector operator-(const Vector &v) const;
    Vector operator-() const;
    Vector operator*(double n) const;
    //friends
    friend Vector operator*(double n, const Vector &v);
    friend ostream & operator<<(ostream &os, const Vector &v);
};//end class Vector
#endif

//部分函数定义省略
//.........
ostream & operator<<(ostream &os, const Vector &v)
{
    if(v.mode == 'r')
        os << "(x,y)=(" << v.x << "," << v.y << ")";
    else if(v.mode == 'p')
        os << "(m,a)=(" << v.mag << "," << v.ang*Rad_to_deg << ")";
    else
        os << "Vector object mode is invalid.";

    return os;
}

这里编译器报错，说不能访问私有成员是怎么回事？明明定义为友元的...