What's the opposite of a cross product? For example, $a \times b = c$
If you only know $a$ and $c$, what method can you use to find $b$?

As Fabian wrote, $b$ is not uniquely determined by $a$ and $c$.  Moreover, there is no solution unless $a$ and $c$ are orthogonal.  If $a$ and $c$ are orthogonal, then the solutions are $(c \times a)/(a\, . a) + t a$ for arbitrary scalars $t$.  
