A proof in vectors If it is given that:
$$ \vec{R} + \dfrac{\vec{R}\cdot(\vec{B}\times(\vec{B}\times\vec{A}))} {|\vec{A} \times \vec{B} |^2}\vec{A} + \dfrac{\vec{R}\cdot(\vec{A}\times(\vec{A}\times\vec{B}))} {|\vec{A} \times \vec{B} |^2}\vec{B} = \dfrac{K(\vec{A}\times\vec{B})} {|\vec{A} \times \vec{B} |^2} $$
then prove that $$K= [ \vec{R} \vec{A} \vec{B} ]$$
I don't know how to even begin. Any ideas?

Start from dot product of both sides by $\vec{A}\times\vec{B}$.
