If vectors $\to A = cos w t^i + sin w t^j$ and $\to B = cos w t / 2^i + sin w t / 2^j$ are functions of time , then the value of $t$ at which they are orthogonal to each other is

t = 0

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t = \frac{π}{4 ω}

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t = \frac{π}{2 ω}

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t = \frac{π}{ω}

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Solution

The correct option is D $t = \frac{π}{ω}$
$\to A . \to B = (cos w t^i + sin w t^j) . (cos \frac{w t}{2}^i + sin \frac{w t}{2}^j)$
$= cos (w t - \frac{w t}{2})$
When they are orthogonal $\to A . \to B = 0$
=> $cos (w t - \frac{w t}{2}) = 0$
$cos (\frac{w t}{2}) = 0$
$\frac{w t}{2} = \frac{π}{2}$
$t = \frac{π}{w}$

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