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Prove that S*(PxQ) = P*(QxS)
where * is dot product and x is cross product
Please see the attached file.
From the cross product definition:
PxQ=(PyQz-PzQy)i + (PzQx-PxQz)j +(PxQy-PyQx)k.
(i j k )
PxQ= det (Px Py Pz
The solution is in the attachment, step-by-step, with brief explanations.