cross(a, b, axisa=-1, axisb=-1, axisc=-1, axis=None)
The cross product of a
and b
in $R^3$
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 z-component of the cross product is returned.
Supports full broadcasting of the inputs.
Components of the first vector(s).
Components of the second vector(s).
Axis of a
that defines the vector(s). By default, the last axis.
Axis of b
that defines the vector(s). By default, the last axis.
Axis of c
containing the cross product vector(s). Ignored if both input vectors have dimension 2, as the return is scalar. By default, the last axis.
If defined, the axis of a
, b
and c
that defines the vector(s) and cross product(s). Overrides :None:None:`axisa`
, :None:None:`axisb`
and :None:None:`axisc`
.
Vector cross product(s).
Return the cross product of two (arrays of) vectors.
inner
Inner product
ix_
Construct index arrays.
outer
Outer product.
Vector cross-product.
>>> 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) array(-3)
Multiple vector cross-products. Note that the direction of the cross product vector is defined by the :None:None:`right-hand 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 :None:None:`axisc`
keyword.
>>> np.cross(x, y, axisc=0) array([[-3, 3], [ 6, -6], [-3, 3]])
Change the vector definition of x
and :None:None:`y`
using :None:None:`axisa`
and :None:None:`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]])See :
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