If `theta` is an acute angle and the vector `(sintheta) hat i+(costheta) hat j` is perpendicular to the vector ` hat i-sqrt(3) hat j ,\ t h e n\ theta=` `pi/6` b. `pi/5` c. `pi/4` d. `pi/3`

Explanation

The correct option is `(d) frac{pi}{3}`

The given vectors are perpendicular. So, their dot product is zero .

`{[(sin theta) hat{i}+(cos theta) hat{j}] cdot(hat{i}-sqrt{3} hat{j})=0} `

`Rightarrow sin theta-sqrt{3} cos theta=0 `

`Rightarrow sin theta=sqrt{3} cos theta `

`Rightarrow tan theta=sqrt{3} `

`Rightarrow theta=frac{pi}{3}(text { Because } theta text { is acute })`