Find the point of intersection of two 3D line segments, works in 2D if z=0

fine-intersect.cpp

// Assume Coord has members x(), y() and z() and supports arithmetic operations
// that is Coord u + Coord v = u.x() + v.x(), u.y() + v.y(), u.z() + v.z()

inline Point
dot(const Coord& u, const Coord& v) 
{
	return u.x() * v.x() + u.y() * v.y() + u.z() * v.z();   
}

inline Point
norm2( const Coord& v )
{
	return v.x() * v.x() + v.y() * v.y() + v.z() * v.z();
}

inline Point
norm( const Coord& v ) 
{
	return sqrt(norm2(v));
}

inline
Coord
cross( const Coord& b, const Coord& c) // cross product
{
	return Coord(b.y() * c.z() - c.y() * b.z(), b.z() * c.x() - c.z() * b.x(), b.x() *  c.y() - c.x() * b.y());
}

bool 
intersection(const Line& a, const Line& b, Coord& ip)
// TODO: To work in 2D set z components to zero
{
Coord da = a.second - a.first; 
Coord db = b.second - b.first;
Coord dc = b.first - a.first;

if (dot(dc, cross(da,db)) != 0.0) // lines are not coplanar
    return false;

	Point s = dot(cross(dc,db),cross(da,db)) / norm2(cross(da,db));
	if (s >= 0.0 && s <= 1.0)
	{
	    ip = a.first + da * Coord(s,s,s);
	    return true;
	}

	return false;
}

This does not work for (0, 0, 0) -> (10, 0, 0) and (9, 0, 0) -> (20, 0, 0). In this case s is not defined since norm2 returns 0.