# Proving Vectors

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

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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