If `veca bot vecb` then vector `vecv` in terms of `veca and vecb` satisfying the equations `vecv. Veca = 0 nad vecv. Vecb = 1 and [ veca veca vecb] =1` is

Options

A. `(vecb)/(|vecb|^(2))+(vecaxxvecb)/(|vecaxxvecb|^(2))`
B. `(vecb)/(|vecb|)+(vecaxxvecb)/(|vecaxxvecb|^(2))`
C. `(vecb)/(|vecb|^(2))+(vecaxxvecb)/(|vecaxxvecb|)`
D. none of these

Answer

A

Explanation

If `veca, vecb, vecc` are three non coplanar vectors, then any vector `vecr` can be expressed as
`vecr={(vecr.veca)/(|veca|^(2))}veca+{(vecr.vecb)/(|vecb|^(2))}+vecb+{(vecr.vecc)/(|vecc|^(2))}vecc`
Clearly `veca, vecb` and `vecaxxvecb` are three non-coplanar vectors.
`:.vecv={(vecv.veca)/(|veca|^(2))}veca+{(vecv.vecb)/(|vecb|^(2))}vecb+{(vecv.(vecaxxvecb))/(|vecaxxvecb|^(2))}(vecaxxvecb)`
`implies vecv=0veca+1/(|vecb|^(2)).vecb+1/(|vecaxxvecb|^(2)).(vecaxxvecb)`