I wanted to proof the property that box product of three vectors remain equal if we change vectors in cyclic manner.
i.e. $$(\vec{a}\times \vec{b}).\vec{c}=(\vec{b}\times \vec{c}).\vec{a}=(\vec{c}\times \vec{a}).\vec{b}$$
I tried to proof using geometry (parallelepiped) and was successful in proving that $(\vec{a}\times \vec{b}).\vec{c}=(\vec{b}\times \vec{c}).\vec{a}\space\space$ but I wasn't able to proof $(\vec{a}\times \vec{b}).\vec{c}=(\vec{c}\times \vec{a}).\vec{b}$
Please explain how can I prove this using geometry (if possible).
Alternative proofs are also welcomed.