If `overset(to)(a) = (hat(i) + hat(j) + hat(k)) , overset(to)(a) .overset(to)(b) =1 " and " overset(to)(a) xx overset(to)(b) = hat(j) - hat(k), " then " overset(to)(b)` is equal to

Options

A. `hat(i) - hat(j) + hat(k)`
B. `2hat(j) - hat(k)`
C. `hat(i)`
D. `2hat(i)`

Answer

C

Explanation

We know that `vec(a) xx (vec(a) xx vec(b)) = (vec(a) ". " vec(b)) vec(a) - (vec(a) ". " vec(b)) vec(b) `
` :. (hat(i) + hat(j) + hat(k)) xx (hat(j) - hat(k) ) = (hat(i) + hat(j) + hat(k)) - (sqrt(3))^(2) vec(b)`
`rArr - 2hat(i) + hat(j) + hat(k) = hat(i) + hat(j) + hat(k) - 2vec(b) rArr 3 vec(b) = + 3hat(i)`
`:. vec(b) = hat(i)`