Программа на классы

#include <cmath>
#include <iostream>
#include <iomanip>
 
const double EPSILON = 0.00001;
 
class Vector {
 public:
  Vector() : x(0), y(0), z(0), length(0) {}
  Vector(const double &x, const double &y, const double &z)
    : x(x), y(y), z(z), length(0) {
    length = sqrt(x * x + y * y + z * z);
  }
  const double &getX() const { return x; }
  const double &getY() const { return y; }
  const double &getZ() const { return z; }
  const double &getLength() const { return length; }
  Vector getNormalized() const {
    return Vector(x / length, y / length, z / length);
  }
  bool isZero() const {
    return getX() < EPSILON && getY() < EPSILON && getZ() < EPSILON;
  }
 private:
  double x, y, z;
  double length;
};
 
std::ostream &operator<<(std::ostream &stream, const Vector &vector) {
  return stream << std::fixed << std::setprecision(4) << "[" <<
    vector.getX() << ";" << vector.getY() << ";" <<
    vector.getZ() << "]";
};
 
bool operator==(const Vector &a, const Vector &b) {
  return (fabs(a.getX() - b.getX()) < EPSILON ) &&
    (fabs(a.getY() - b.getY()) < EPSILON ) &&
    (fabs(a.getZ() - b.getZ()) < EPSILON );
};
 
Vector operator+(const Vector &a, const Vector &b) {
  return Vector(a.getX() + b.getX(), a.getY() + b.getY(),
    a.getZ() + b.getZ());
}
 
Vector operator-(const Vector &a) {
  return Vector(-a.getX(), -a.getY(), -a.getZ());
}
 
Vector operator-(const Vector &a, const Vector &b) {
  return Vector(a.getX() - b.getX(), a.getY() - b.getY(),
    a.getZ() - b.getZ());
}
 
double operator%(const Vector &a, const Vector &b) {
  return a.getX() * b.getX() + a.getY() * b.getY() + a.getZ() * b.getZ();
}
 
Vector operator*(const Vector &a, const Vector &b) {
  return Vector(a.getY() * b.getZ() - a.getZ() * b.getY(),
    a.getZ() * b.getX() - a.getX() * b.getZ(),
    a.getX() * b.getY() - a.getY() * b.getX());
}
 
bool operator||(const Vector &a, const Vector &b) {
  return a.isZero() || b.isZero() || (a * b).isZero() ||
    (fabs(a.getX() / b.getX() - a.getY() / b.getY()) < EPSILON &&
    fabs(a.getY() / b.getY() - a.getZ() / b.getZ()) < EPSILON);
};
 
int main(int argc, char **argv) {
  Vector a(2, 3, 1), b(0, -1, 5), c(4, 6, 2);
  std::cout << "(" << a << " + " << b << ") x " << c << " = " <<
    ((a + b) * c) << std::endl;
  std::cout << "(" << a << " + " << b << ") * " << c << " = " <<
    ((a + b) % c) << std::endl;
  std::cout << a << " * " << b << " = " <<
    (a % b) << std::endl;
  std::cout << a << " is " << ((a || b) ? "" : "not ") <<
    "collinear to " << b << std::endl;
  std::cout << a << " is " << ((a || c) ? "" : "not ") <<
    "collinear to " << c << std::endl;
  return 0;
};