Vector equations, possible to solve for x?

Hello there,



In scalar algebra, I find solving for variables a useful tool. Say ohms law, I want to find ##R## so:



$$

U=RI \iff R = \frac{U}{I}

$$



Can I do something analogous in vector equations? I.e. May I solve for ##\vec{\omega}## in equations using cross or dot products?



$$

\vec{v} = \vec{\omega} \times \vec{r} \iff \vec{\omega} = ?

$$



or:



$$

\vec{\alpha} \cdot \vec{\beta} = \gamma \iff \vec{\beta} = ?

$$





It would be fantastic if I could solve for vectors in some way.



Hope you are able to help.



Thank you for your time!



Kind regards,

Marius