If `vec(alpha)=x(vecaxxvecb)+y(vecbxxvecc)+z(veccxxveca)` and `[veca vecb vecc]=1/8`, then `x+y+z=`

Options

A. `8vec(alpha).(veca+vecb+vecc)`
B. `vec(alpha).(veca+vecb+vecc)`
C. `8(veca+vecb+vecc)`
D. None of these

Answer

A

Explanation

We have
`vec(alpha)=x(vecaxxvecb)+y(vecbxxvecc)+z(veccxxveca)`
Taking dot products with `veca, vecb` and `vecc` repectively, we get
`vec(alpha).veca=y[veca vecb vecc]impliesy=8(vec(alpha).veca)`
`vec(alpha).vecb=z[veca vecb vecc]impliesz=8(vec(alpha).vecb)`
and `vec(alpha).vecc=x[veca vecb vecc]=x=8(vec(alpha).vecc)`
`:.x+y+z=8vec(alpha).(veca+vecb+vecc)`