Evaluate the following: `[ hat i\ hat j\ hat k]+[ hat j\ hat k\ hat i]+[ hat k\ hat i\ hat j]` .

Explanation

We know that

`[hati hatj hatk]=(hati xx hatj)*hatk`

`hati*hati=1`

`hati xx hatj=hatk`, `hatj xx hatk=hati`, `hatk xx hati=hatj`

Apply to the given question

`[hati hatj hatk] + [hatj hatk hati] + [hatk hati hatj]`

`= (hati xx hatj)*hatk +(hatj xx hatk)*hati + (hatk xx hati)*hatj`

`= hatk*hatk + hati*hati + hatj*hatj`

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