If `alpha=x(a xxb)+y(b xxc)+z(cxxa) and [abc]=(1)/(8)`, then x+y+z is equal to

Options

A. `8alpha*(a+b+c)`
B. `alpha*(a+b+c)`
C. `8(a+b+c)`
D. None of these

Answer

A

Explanation

We have, `alpha=x(axxb)+y(bxxc)+z(cxxa)`
Taking dot product with
a,b,c respectively, we get
`alpha*a=y[abc]`
`impliesy=8(alpha*a)`
`alpha*b=z((cxxa)*b)`
`alpha*b=z[abc]`
`impliesz=8(alpha*beta)`
`alpha*c=x[axxbxxc]`
`alpha*c=x[abc]`
`impliesx=8(alpha*c)`
`thereforex+y+z=8alpha*(axxbxxc)`