Find the value of `theta(0,pi//2)` for which vectors ` vec a=(sintheta) hat i+(costheta) hat j a n d\ vec b= hat i-sqrt(3) hat j+2 hat k` are perpendicular.

Explanation

Given: `vec{a}=(sin theta) hat{i}+(cos theta) hat{j`}


Given: `vec{b}=hat{i}-sqrt{3} hat{j}+2 hat{k}`


vectors are perpendicular (given)


`Rightarrow vec{a} cdot vec{b}=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}`