If vectors \( \overrightarrow{\mathrm{A}}=\cos \omega \mathrm{t} \hat{i}+\sin \omega \mathrm{t} ...

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If vectors \( \overrightarrow{\mathrm{A}}=\cos \omega \mathrm{t} \hat{i}+\sin \omega \mathrm{t} \hat{j} \) and \( \overrightarrow{\mathrm{B}}=\cos \frac{\omega \mathrm{t}}{2} \hat{i}+\sin \frac{\omega \mathrm{t}}{2} \hat{j} \) are functions of time, then the value of \( t \) at which they are orthogonal to each other is:
(1) \( t=0 \)
(2) \( \mathrm{t}=\frac{\pi}{4 \omega} \)
(3) \( t=\frac{\pi}{2 \omega} \)
(4) \( \mathrm{t}=\frac{\pi}{\omega} \)
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