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

• A

  $t=\frac{\pi }{2\omega }$
• Correct answer
  B

  $t=\frac{\pi }{\omega }$
• C

  $t=0$
• D

  $t=\frac{\pi }{4\omega }$

Hence, the correct answer is option: 'B'.