class Vector {

private:

  double i, j, k;

public:

  // creates a vector containing 0i + 0j + 0k
  Vector ();

  // creates a vector with specfied i, j and k coefficients
  Vector (double i, double j, double k);

  // returns magnitude of vector
  double magnitude () const;

  // returns dot product of vector and another vector
  // (returns vector . other vector)
  double dot (const Vector &otherVector) const;

  // returns cross produce of vector and another vector
  // (returns vector X other vector)
  Vector cross (const Vector &otherVector) const;

  // adds another vector to a vector 
  // (returns = vector + other vector)
  void add (const Vector &otherVector);

  // converts a vector to a unit vector while preserving its direction.
  // throws a domain_error exception if the vector has magnitude zero.
  void unitize ();

  // reads a vector (i, j, and k) from the given input stream
  void read (istream &is);

  // writes a vector to the given output stream in format "i"i + "j"j + "k"k
  void write (ostream &os);

};