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I have following problem of double dot product [tex](\vec a \cdot \vec b)(\vec a^* \cdot \vec c),[/tex] and I have expected rusult [tex]|a|^2(\vec b \cdot \vec c),[/tex] but I don't know if it is the exactly result (I am unable to find any appropriate identity or proove it), or it is just an approximation... where [tex]\vec a[/tex] is complex and [tex]\vec b, \vec c[/tex] are real 3D vectors. Maybe can help, that all vectors lie in the plane. So is it true that

[tex](\vec a \cdot \vec b)(\vec a^* \cdot \vec c) =? |a|^2(\vec b \cdot \vec c)?[/tex]

Thanks,

Michal

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# Double dot product

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