Return the cross product of two (arrays of) vectors.
The cross product of a and b in is a vector perpendicular to both a and b. If a and b are arrays of vectors, the vectors are defined by the last axis of a and b by default, and these axes can have dimensions 2 or 3. Where the dimension of either a or b is 2, the third component of the input vector is assumed to be zero and the cross product calculated accordingly. In cases where both input vectors have dimension 2, the zcomponent of the cross product is returned.
Parameters:  a : array_like
b : array_like
axisa : int, optional
axisb : int, optional
axisc : int, optional
axis : int, optional


Returns:  c : ndarray

Raises:  ValueError :

Examples
Vector crossproduct.
>>> x = [1, 2, 3]
>>> y = [4, 5, 6]
>>> np.cross(x, y)
array([3, 6, 3])
One vector with dimension 2.
>>> x = [1, 2]
>>> y = [4, 5, 6]
>>> np.cross(x, y)
array([12, 6, 3])
Equivalently:
>>> x = [1, 2, 0]
>>> y = [4, 5, 6]
>>> np.cross(x, y)
array([12, 6, 3])
Both vectors with dimension 2.
>>> x = [1,2]
>>> y = [4,5]
>>> np.cross(x, y)
3
Multiple vector crossproducts. Note that the direction of the cross product vector is defined by the righthand rule.
>>> x = np.array([[1,2,3], [4,5,6]])
>>> y = np.array([[4,5,6], [1,2,3]])
>>> np.cross(x, y)
array([[3, 6, 3],
[ 3, 6, 3]])
The orientation of c can be changed using the axisc keyword.
>>> np.cross(x, y, axisc=0)
array([[3, 3],
[ 6, 6],
[3, 3]])
Change the vector definition of x and y using axisa and axisb.
>>> x = np.array([[1,2,3], [4,5,6], [7, 8, 9]])
>>> y = np.array([[7, 8, 9], [4,5,6], [1,2,3]])
>>> np.cross(x, y)
array([[ 6, 12, 6],
[ 0, 0, 0],
[ 6, 12, 6]])
>>> np.cross(x, y, axisa=0, axisb=0)
array([[24, 48, 24],
[30, 60, 30],
[36, 72, 36]])