If `vec(alpha)=2hati+3hatj-hatk, vec(beta)=-hati+2hatj-4hatk, vecgamma=hati+hatj+hatk`, then `(vec(alpha)xxvec(beta)).(vec(alpha)xxvec(gamma))` is equal to

Options

A. `-74`
B. `74`
C. `64`
D. `60`

Answer

A

Explanation

We have
`(vec(alpha)xxvec(beta)).(vec(alpha)xxvecgamma))=(vec(alpha).vec(alpha)(vec(beta).vec(gamma))-(vec(alpha).vec(gamma))(vec(beta).vec(alpha))`
`implies(vec(alpha)xxvec(beta)).(vec(alpha)xxvec(gamma))=-3xx14-8xx4=-42-32=-74`