Ayuda para demostrar que si a, b y c están en V3, entonces(axb) · [ (bxc) x (cxa) ] = [a · (bxc) ] ^ 2No estoy segura del procedimiento : /?

Utilizaré esta propiedad <img src="https://tex.z-dn.net/?f=p%5Ctimes%28q%5Ctimes%20r%29%3Dq%28p%5Ccdot%20r%29-r%28p%5Ccdot%20q%29" />

<img src="https://tex.z-dn.net/?f=E%3D%28a%5Ctimes%20b%29%5Ccdot%5B%28b%5Ctimes%20c%29%5Ctimes%28c%5Ctimes%20a%29%5D%5C%5C%20%5C%5C%0AE%3D%28a%5Ctimes%20b%29%5Ccdot%5Cleft%5C%7Bc%5C%2C%5B%28b%5Ctimes%20c%29%5Ccdot%20a%5D-a%5C%2C%5B%28b%5Ctimes%20c%29%5Ccdot%20c%5D%5Cright%5C%7D%5C%5C%20%5C%5C%0AE%3D%28a%5Ctimes%20b%29%5Ccdot%5Cleft%5C%7Bc%5C%2C%5B%28b%5Ctimes%20c%29%5Ccdot%20a%5D%5Cright%5C%7D%5C%5C%20%5C%5C%0AE%3D%5B%28a%5Ctimes%20b%29%5Ccdot%20c%5D%5C%2C%5B%28b%5Ctimes%20c%29%5Ccdot%20a%5D%5C%5C%20%5C%5C%0AE%3D%5B-%28b%5Ctimes%20a%29%5Ccdot%20c%5D%5C%2C%5B%28b%5Ctimes%20c%29%5Ccdot%20a%5D%5C%5C%20%5C%5C%0AE%3D%5B%28b%5Ctimes%20c%29%5Ccdot%20a%5D%5C%2C%5B%28b%5Ctimes%20c%29%5Ccdot%20a%5D%5C%5C%20%5C%5C%0A%5Cboxed%7BE%3D%5B%28b%5Ctimes%20c%29%5Ccdot%20a%5D%5E2%7D" />.