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If vec(a) = hat(i) + hat(j) - hat(k), ve...

If `vec(a) = hat(i) + hat(j) - hat(k), vec(b)= hat(i) - hat(j) + hat(k) and vec(c )` is unit vector perpendicular to `vec(a)` and coplanar with `vec(a) and vec(b)`, then unit vector `vec(d)` perpendicular to both `vec(a) and vec(c )` is

A

`pm (1)/(sqrt6) (2 hat(i) - hat(j) + hat(k))`

B

`pm (1)/(sqrt2) (hat(j) + hat(k))`

C

`pm (1)/(sqrt6) (hat(i) - 2hat(j) + hat(k))`

D

`pm (1)/(sqrt2) (hat(j) - hat(k))`

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