Let `hatu, hatv, hatw` be three unit vectors such that `hatu+hatv+hatw=hata, hata.hatu=3/2, hata.hatv=7/4` & `|hata|=2`, then

Options

A. `hatu. hatv=3/4`
B. `hatu.hatw=0`
C. `hatu. hatv=1/4`
D. `hatu.hatw=-1/4`

Answer

A, D

Explanation

`hatu.hatv+hatu.hatw=1/2`…(ii) (taking dot product with `hatu,hatv` & `hata`)
`hatu.hatv+hatv.hatw=3/4`………(iii)
`hata.hatw=3/4`…………..(iv)
Again taking dot product with `hatw` we get `hatu.hatw+hatv.hatw+|hatw|^(2)=hata.hatw`
`hatu.hatw+hatu.hatw+1=3/4`
`hatu.hatw+hatu.hatw=(-1)/4`............(v)
on adding (ii),(iii),(v)
`hatu.hatv+hatv.hatw+hatu.hatw=1/2`
on substrating equation (ii) from (iv)
`hatv.hatw=0`