If vectors → A = cosωt ˆ i + sinωt ˆ j A→=cosωti^+sinωtj^ and → B = cos ωt 2 ˆ i + sin ωt 2 ˆ j B→=cos ωt2i^+sin ωt2j^ are functions of time, then the value of t at which they are orthogonal to each other

 

 From NCERT NEET - 2015

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

1. $t=\frac{\pi }{4\omega }$

2. $t=\frac{\pi }{2\omega }$

3. $t=\frac{\pi }{\omega }$

4. $t=0$