Physics - Vectors Question with Solution | TestHub

$\overrightarrow{\mathrm{A}}=\cos wt\widehat{\mathrm{i}}+\sin wt\widehat{\mathrm{j}}$
$\overrightarrow{B}=cos\frac{wt}{2}\widehat{i}+sin\frac{wt}{2}\widehat{j}$
For these vectors to be orthogonal,$\overrightarrow{A}·\overrightarrow{B}=0$
$\overrightarrow{A}·\overrightarrow{B}=0=\cos wt.\cos \frac{wt}{2}+\sin wt.\sin \frac{wt}{2}$
$=\cos \left(wt-\frac{wt}{2}\right)=\cos \left(\frac{wt}{2}\right)=0$
So, as we know, $\cos (90)=0$.
So,$\frac{wt}{2}=\frac{\pi }{2}\Rightarrow t=\frac{\pi }{w}$