Cross product
Cross product inverse

For the cross product a × b = c, there are multiple b vectors that give the same value of c. As a result, it is not possible to rearrange this equation to yield a unique solution for b in terms of a and c. Nevertheless, it is possible to find a family of solutions for b, which are

where t is an arbitrary constant.

This can be derived using the triple product expansion:

Rearrange to solve for b to give

The coefficient of the last term can be simplified to just the arbitrary constant t to yield the result shown above.
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