If vectors $\overrightarrow{A} = \cos \omega \hat{i} + \sin \omega \hat{j} $ and $\overrightarrow{B} = \cos \frac{\omega t}{2} \hat{i} + \sin \frac{\omega t}{2} \hat{j} $ are functions of time, then the value of $t$ at which they are orthogonal to each other is :

Question

( A ) $t = \frac{\pi}{4\omega}$
( B ) $t = \frac{\pi}{2\omega}$
( C ) $t = 0$
( D ) $t = \frac{\pi}{\omega}$