prove that `(veca.hati)(vecaxxhati)+(veca.hatj)(vecaxxhatj)+(veca.hatk)(vecaxxhatk)=vec0`

Explanation

Let `veca = a_(1) hati + a_(2)hatj + a_(3) hatk`1, therefore,
`veca. hati = (a_(1) hati = a_(2) and veca . Hatk = a_(3)`
`and vecaxxhati = (a_(1)hati+a_(2)hat j + a_(3) hatk) xx hati = a_(2)hatk + a_(3) hatj` ,
`(veca . hati ) (vecaxx hati) + (veca . hatj) (veca xx hatj) + (veca. hatk) (veca xx veck)`
`-a_(1)a_(2)hatk + a_(1)a_(3)hatj + a_(1)a_(2) hatk +a_(3)a_(2)hati`
`+a_(3)a_(2) hati -a_(3)a_(1)hati`
`vec0`