OK, i am trying to prove that if $\vec a\times \vec b = \vec a \times \vec c$ and also $\vec a\cdot \vec b = \vec a \cdot \vec c$ then $\vec b = \vec c$.
so far i got to $\vec n \tan \alpha = \vec m \tan \beta$ and do not know how to continue to get the result
this seems too easy :)