For any two vectors a and b, find a.(b x a).
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\(\vec a.(\vec b\times \vec a)=0\)
We know,
\((\vec b\times \vec a)\) is perpendicular to both \(\vec a\) and \(\vec b\).
So, \(\vec a.(\vec b\times \vec a)=0\)
[\(\because\vec a\) and \((\vec b\times\vec a)\) are perpendicular to each other]