issues: 489034521

xarray currently has the xarray.dot() function for calculating arbitrary dot products which is indeed very handy. Sometimes, especially for physical applications I also need a vector cross product. I' wondering whether you would be interested in having xarray.cross as a wrapper of numpy.cross. I currently use the following implementation:

```python def cross(a, b, spatial_dim, output_dtype=None): """xarray-compatible cross product

Compatible with dask, parallelization uses a.dtype as output_dtype
"""
# TODO find spatial dim default by looking for unique 3(or 2)-valued dim?
for d in (a, b):
    if spatial_dim not in d.dims:
        raise ValueError('dimension {} not in {}'.format(spatial_dim, d))
    if d.sizes[spatial_dim] != 3:  #TODO handle 2-valued cases
        raise ValueError('dimension {} has not length 3 in {}'.format(d))

if output_dtype is None: 
    output_dtype = a.dtype  # TODO some better way to determine default?
c = xr.apply_ufunc(np.cross, a, b,
                   input_core_dims=[[spatial_dim], [spatial_dim]], 
                   output_core_dims=[[spatial_dim]], 
                   dask='parallelized', output_dtypes=[output_dtype]
                  )
return c

```

Example usage

python import numpy as np import xarray as xr a = xr.DataArray(np.empty((10, 3)), dims=['line', 'cartesian']) b = xr.full_like(a, 1) c = cross(a, b, 'cartesian')

Main question

Do you want such a function (and possibly associated DataArray.cross methods) in the xarray namespace, or should it be in some other package? I didn't find a package which would be a good fit as this is close to core numpy functionality and isn't as domain specific as some geo packages. I'm not aware of some "xrphysics" package.

I could make a PR if you'd want to have it in xarray directly.

Output of xr.show_versions()