Vector3d

#include <iostream>
#include <conio.h>
using namespace std;
struct Point {
    using point_t = tuple<double, double, double>;
    double x;
    double y;
    double z;
    Point() : x(0), y(0), z(0) {}
    Point(double x, double y, double z) : x(x), y(y), z(z) {}
    double length(const Point& p)const {
        return sqrt(pow(p.x - x, 2) + pow(p.y - y, 2) + pow(p.z - z, 2));
    }
    friend istream& operator>>(istream& in, Point& p) {
        cout << "x: ";
        in >> p.x;
        cout << "y: ";
        in >> p.y;
        cout << "z: ";
        in >> p.z;
        return in;
    }
    friend ostream& operator<<(ostream& out, const Point& p) {
        return out << "{ " << p.x << ", " << p.y << ", " << p.z << " }";
    }
};
class Vector3d {
public:
    Vector3d() : p_(Point{}) {}
    Vector3d(const Point p) : p_(p) {}
    void set(const Point p) {
        p_ = p;
    }
    double length()const {
        Point p;
        return p_.length(p);
    }
private:
    Point p_;
    friend Vector3d operator+(const Vector3d& a, const Vector3d& b) {
        Point p;
        p.x = a.p_.x + b.p_.x;
        p.y = a.p_.y + b.p_.y;
        p.z = a.p_.z + b.p_.z;
        return { p };
    }
    friend Vector3d operator-(const Vector3d& a, const Vector3d& b) {
        Point p;
        p.x = a.p_.x - b.p_.x;
        p.y = a.p_.y - b.p_.y;
        p.z = a.p_.z - b.p_.z;
        return { p };
    }
    friend double operator*(const Vector3d& a, const Vector3d& b) {
        return a.p_.x * b.p_.x + a.p_.y * b.p_.y + a.p_.z * b.p_.z;
    }
    friend Vector3d operator*(const Vector3d& v, const double n) {
        Point p;
        p.x = v.p_.x * n;
        p.y = v.p_.y * n;
        p.z = v.p_.z * n;
        Vector3d t(p);
        return t;
    }
    friend Vector3d operator*(const double n, const Vector3d& v) {
        Point p;
        p.x = v.p_.x * n;
        p.y = v.p_.y * n;
        p.z = v.p_.z * n;
        Vector3d t(p);
        return t;
    }
    friend bool operator<(const Vector3d& a, const Vector3d& b) {
        return a.length() < b.length();
    }
    friend bool operator==(const Vector3d& a, const Vector3d& b) {
        return a.length() == b.length();
    }
    friend bool operator!=(const Vector3d& a, const Vector3d& b) {
        return !(a == b);
    }
    friend bool operator<=(const Vector3d& a, const Vector3d& b) {
        return a < b || a == b;
    }
    friend bool operator>(const Vector3d& a, const Vector3d& b) {
        return !(a <= b);
    }
    friend bool operator>=(const Vector3d& a, const Vector3d& b) {
        return !(a < b);
    }
    friend istream& operator>>(istream& in, Vector3d& v) {
        return in >> v.p_;
    }
    friend ostream& operator<<(ostream& out, const Vector3d& v) {
        return out << v.p_;
    }
};
void start_menu() {
    system("cls");
    puts("1) ввод векторов");
    puts("2) вывод векторов");
    puts("3) сумма векторов");
    puts("4) разность векторов");
    puts("5) умножение векторов");
    puts("6) сравнение векторов");
    puts("7) очистить содержимое");
    puts("0) выход из программы");
}
void compare(const Vector3d& a, const Vector3d& b) {
    if (a == b) {
        cout << a << " == " << b << '\n';
        cout << a << " <= " << b << '\n';
        cout << a << " => " << b << '\n';
    } else {
        cout << a << " != " << b << '\n';
        if (a < b) cout << a << " < " << b << '\n';
        else cout << a << " > " << b << '\n';
    }
}
int main() {
    system("chcp 1251 > nul");
    while (true) {
        start_menu();
        Vector3d a, b;
        auto flag = false;
        char point;
        while (true) {
            switch (point = _getch()) {
            case '0':  return 0;
            case '1': cin >> a >> b; break;
            case '2': cout << a << '\n' << b << '\n'; break;
            case '3': cout << "Сумма: " << a + b << '\n'; break;
            case '4': cout << "Разность: " << a - b << '\n'; break;
            case '5': cout << "Произведение: " << a * b << '\n'; break;
            case '6': compare(a, b); break;
            case '7': flag = !flag; break;
            default: puts("Вы ошиблись при выборе пункта меню!\a");
            }
            if (flag) break;
        }
    }
}