A vector `sqrt(3)hati + hatj` rotates about its tail through an angle `30^(@)` in clock wise direction then the new vector is

Explanation

The magnitude of `sqrt(3) hat(i) + hat(j)` is `sqrt(3+1) = 2` The angle made by the vector with x-axis is
`Tan theta = (A_(y))/(A_(x)) = (1)/(sqrt(3))`
`therefore theta = 30^(@)`

When the given vector rotates `30^(@)` in clock wise is directions changes along x-axis but its magnitude does not change.
`therefore` The new vector is `2hat(i)`