My Solution:
// Vector3D.h
#include <string>
#include <sstream>
#include <math.h>
namespace VectorLibrary
{
class Vector3D
{
public:
Vector3D() : _x(0.0), _y(0.0), _z(0.0) {}
Vector3D(const Vector3D& r) : _x(r._x), _y(r._y), _z(r._z) {}
Vector3D(double x, double y, double z) : _x(x), _y(y), _z(z) {}
~Vector3D() {}
Vector3D& operator= (const Vector3D& r)
{
SetX(r.GetX());
SetY(r.GetY());
SetZ(r.GetZ());
return *this;
}
double GetX() const { return _x; }
double GetY() const { return _y; }
double GetZ() const { return _z; }
void SetX(double x) { _x = x; }
void SetY(double y) { _y = y; }
void SetZ(double z) { _z = z; }
double Magnitude()
{
return sqrt((_x * _x) + (_y * _y) + (_z * _z));
}
void Normalize()
{
double mag = Magnitude();
if (mag > 0)
{
_x /= mag;
_y /= mag;
_z /= mag;
}
}
std::string asString()
{
std::stringstream s;
s << "(" << _x << ", " << _y << ", " << _z << ")";
return s.str();
}
private:
double _x;
double _y;
double _z;
};
inline Vector3D ScalarMultiply(double scalar, const Vector3D& v)
{
Vector3D vTemp(scalar * v.GetX(), scalar * v.GetY(), scalar * v.GetZ());
return vTemp;
}
// for convienence
inline Vector3D operator* (double scalar, const Vector3D& v)
{
return ScalarMultiply(scalar, v);
}
inline Vector3D operator* (const Vector3D& v, double scalar)
{
return ScalarMultiply(scalar, v);
}
inline Vector3D& operator*=(Vector3D& v, double scalar)
{
v = ScalarMultiply(v, scalar);
return v;
}
inline Vector3D operator- (const Vector3D& l, const Vector3D& r)
{
Vector3D v(l.GetX() - r.GetX(), l.GetY() - r.GetY(), l.GetZ() - r.GetZ());
return v;
}
inline Vector3D& operator-=(Vector3D& l, const Vector3D& r)
{
Vector3D v = l - r;
l = v;
return l;
}
inline Vector3D operator+ (const Vector3D& l, const Vector3D& r)
{
Vector3D v(l.GetX() + r.GetX(), l.GetY() + r.GetY(), l.GetZ() + r.GetZ());
return v;
}
inline Vector3D& operator-=(Vector3D& l, const Vector3D& r)
{
Vector3D v = l + r;
l = v;
return l;
}
inline double DotProduct(const Vector3D& l, const Vector3D& r)
{
double ret = (l.GetX() * r.GetX()) + (l.GetY() * r.GetY()) + (l.GetZ() * r.GetZ());
return ret;
}
inline Vector3D CrossProduct(const Vector3D& l, const Vector3D& r)
{
Vector3D v( (l.GetY() * r.GetZ()) - (l.GetZ() * r.GetY()),
(l.GetZ() * r.GetX()) - (l.GetX() * r.GetZ()),
(l.GetX() * r.GetY()) - (l.GetY() *
