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enter image description here How does one obtain the Eq(1)? Why is there a cross product on the right side?

danny
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    Because there is a cross-product on the left? –  Dec 18 '19 at 13:57
  • "Why is there a cross product in the right-hand side"? Short answer: because there is one in the left-hand side, too. It's just some vector calculus, nothing deep. – Giuseppe Negro Dec 18 '19 at 13:57
  • But how does one derive that? That’s where I’m struggling. – danny Dec 18 '19 at 13:59
  • Write out the cross-product as a determinant: $\vec a\times \vec b=\begin{vmatrix} i&j&k\a_1&a_2&a_3\b_1&b_2&b_3\end{vmatrix}$. –  Dec 18 '19 at 14:03
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    No, don't write it as a determinant! Just multiply out the brackets. Something like in this question: https://math.stackexchange.com/questions/2884982/factorizing-a-cross-product – Hans Lundmark Dec 18 '19 at 15:30

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Pretty straightforward using $a\times a=0, a\times b=-b\times a$ together with $(a+b)\times c=a\times c+b\times c$. And of course $ra\times b=r(a\times b)$.