If vectors `hata, hatb, hatc` are in space such that `hata.hatb=hatb.hatc=hatc.hata=1/2`, then `(hataxxhatb).(hataxx(hatbxxhatc))` is equal to

Options

A. `1/(sqrt(2))`
B. `-1/(sqrt(2))`
C. `1/(2sqrt(2))`
D. `-1/(2sqrt(2))`

Answer

D

Explanation

`:.(hataxxhatb).{(hata.hatb)hatb-(hata.hatb)hatc}=0-(hata.hatb)[(hata, hatb, hatc)]`
`=-1/2xx1/(sqrt(2))`
`:.[(hata, hatb, hatc)]^(2)=|(1, 1/2, 1/2),(1/2, 1, 1/2),(1/2, 1/2, 1)|=1/2`