Relation between cross-product and outer product If inner products ($V$) are generalisations of dot products ($ \mathbb{R}^n$), then are outer products ($V$) also related to cross-products ($ \mathbb{R}^3$) in some way?

A quick search reveals that they are, but yet the outer product of two column vectors in $ \mathbb{R}^3$ is a 3x3 matrix, not another column vector. What's the link? Thanks!
Cross product is much more related to exterior product which is in fact a far going generalization.

Outer product is a matricial description of tensor product of two vectors.
The inner product creates a scalar and the outer a skew-symmetric matrix. If you sum like-terms of this matrix you get a vector which also results from the cross product computation.