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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

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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
...

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