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    Proving Vectors

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    Prove that S*(PxQ) = P*(QxS)
    where * is dot product and x is cross product
    if S=Sxi+Syj+Szk
    P=Pxi+Pyj+Pzk
    Q=Qxi+Qyj+Qzk

    © BrainMass Inc. brainmass.com December 24, 2021, 4:52 pm ad1c9bdddf
    https://brainmass.com/physics/scalar-and-vector-operations/proving-vector-functions-13062

    Solution Preview

    Please see the attached file.

    From the cross product definition:

    PxQ=(PyQz-PzQy)i + (PzQx-PxQz)j +(PxQy-PyQx)k.

    Written conveniently:

    (i j k )
    PxQ= det (Px Py Pz
    ...

    Solution Summary

    The solution is in the attachment, step-by-step, with brief explanations.

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