Question

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

Answer 1

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

(a) $t = \frac{\pi}{2\omega}$

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