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Prove that [vecaxxvecbvecbxxveccveccxxveca] = [vecavecbvecc]^2

Answer»

Solution :`[vecaxxvecbvecbxxveccveccxxveca] = (VECAXXVECB).[vecbxxvec)xx(veccxxveca)]`
[using VECTOR triple product.
=`(vecaxxvecb).{(vecbxxvecc)xxveca)vecc-(vecbxxvecc).vecc)veca}`
= `(vecaxxvecb).{((vecbxxvecc).veca)vecc}[because (vecbxxvecc).vecc = 0]`
=`{vecaxxvecb).vecc} {vecbxxvecc).veca}`
=`{veca.(vecbxxvecc} {veca.(vecbxxvecc)}`
[therefore In scalar triple product dot and cross can be interchanged and dot product is COMMUTATIVE.]
=`{vecavecbvec][vecavecbvecc] = [vecavecbvecc]^2`(Proved).


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