class Vector4d:
	def __init__(self, x, y, z, w):
		self.x = x
		self.y = y
		self.z = z
		self.w = w
		
class Vector3d:
	def __init__(self, x, y, z):
		self.x = x
		self.y = y
		self.z = z
		
	def cross_product(self, vector3d):
		# Returns a line that is perpendicular to the parameter
		# and self.
		# Returns the 'normal'.
		x = self.y * vector3d.z - self.z * vector3d.y
		y = self.z * vector3d.x - self.x * vector3d.z
		z = self.x * vector3d.y - self.y * vector3d.x
		
		return Vector3d(x, y, z)
		
	def dot_product(self, vector3d):
		# Returns a scalar that defines how similar two
		# vectors are to one another.
		return self.x * vector3d.x + self.y * vector3d.y + self.z * vector3d.z
		
class Vector2d:
	def __init__(self, x, y):
		self.x = x
		self.y = y