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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