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Prove that (veca.hati)(vecaxxhati)+(veca...

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

A

` 3veca`

B

`veca`

C

`vec0`

D

`2veca`

Text Solution

Verified by Experts

The correct Answer is:
C
Let `veca =a_(1)hati+a_(2)hati +a_(2)hatj +a_(3)hatk`, Then,
` veca.hati=a_(1),veca.hatj=a_(2), veca.hatk =a_(3)`
` veca xx hati =- a_(2) hatk + a_(2) hatj ,veca xx hatj = a_(1)hatk -a_(3)hati , veca xx hatk = - a_(1)hatk + a_(2)hati `
` (veca .hati) (veca xx hati) + (veca .hatj) (veca xx hatj) + ( veca .hatk) (veca xx hatk)`
` = a_(1) (-a_(2)hatk + a_(3)hatj) + a_(2) (a_(1)hatk -a_(3) hati) + a_(3) (-a_(1)hatj + a_(2)hati) = vec0`
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