Ayuda para demostrar que si a,b y c están en V3, entonces
(axb) · [ (bxc) x (cxa) ] = [a · (bxc) ] ^2
No estoy segura del procedimiento :/
Respuestas a la pregunta
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Utilizaré esta propiedad
![E=(a\times b)\cdot[(b\times c)\times(c\times a)]\\ \\
E=(a\times b)\cdot\left\{c\,[(b\times c)\cdot a]-a\,[(b\times c)\cdot c]\right\}\\ \\
E=(a\times b)\cdot\left\{c\,[(b\times c)\cdot a]\right\}\\ \\
E=[(a\times b)\cdot c]\,[(b\times c)\cdot a]\\ \\
E=[-(b\times a)\cdot c]\,[(b\times c)\cdot a]\\ \\
E=[(b\times c)\cdot a]\,[(b\times c)\cdot a]\\ \\
\boxed{E=[(b\times c)\cdot a]^2}](https://tex.z-dn.net/?f=E%3D%28a%5Ctimes+b%29%5Ccdot%5B%28b%5Ctimes+c%29%5Ctimes%28c%5Ctimes+a%29%5D%5C%5C+%5C%5C%0AE%3D%28a%5Ctimes+b%29%5Ccdot%5Cleft%5C%7Bc%5C%2C%5B%28b%5Ctimes+c%29%5Ccdot+a%5D-a%5C%2C%5B%28b%5Ctimes+c%29%5Ccdot+c%5D%5Cright%5C%7D%5C%5C+%5C%5C%0AE%3D%28a%5Ctimes+b%29%5Ccdot%5Cleft%5C%7Bc%5C%2C%5B%28b%5Ctimes+c%29%5Ccdot+a%5D%5Cright%5C%7D%5C%5C+%5C%5C%0AE%3D%5B%28a%5Ctimes+b%29%5Ccdot+c%5D%5C%2C%5B%28b%5Ctimes+c%29%5Ccdot+a%5D%5C%5C+%5C%5C%0AE%3D%5B-%28b%5Ctimes+a%29%5Ccdot+c%5D%5C%2C%5B%28b%5Ctimes+c%29%5Ccdot+a%5D%5C%5C+%5C%5C%0AE%3D%5B%28b%5Ctimes+c%29%5Ccdot+a%5D%5C%2C%5B%28b%5Ctimes+c%29%5Ccdot+a%5D%5C%5C+%5C%5C%0A%5Cboxed%7BE%3D%5B%28b%5Ctimes+c%29%5Ccdot+a%5D%5E2%7D "E=(a\times b)\cdot[(b\times c)\times(c\times a)]\\ \\
E=(a\times b)\cdot\left\{c\,[(b\times c)\cdot a]-a\,[(b\times c)\cdot c]\right\}\\ \\
E=(a\times b)\cdot\left\{c\,[(b\times c)\cdot a]\right\}\\ \\
E=[(a\times b)\cdot c]\,[(b\times c)\cdot a]\\ \\
E=[-(b\times a)\cdot c]\,[(b\times c)\cdot a]\\ \\
E=[(b\times c)\cdot a]\,[(b\times c)\cdot a]\\ \\
\boxed{E=[(b\times c)\cdot a]^2}")
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