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A unit vector r makes angles \(\cfrac{\pi}3\) and \(\cfrac{\pi}2\) with \(\hat j\)  and \(\hat k\)  respectively and a acute angle θ with  \(\vec i\). Find  θ.

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The sum of squares of direction cosines of a vector is 1.

Let the angles made by vector be α,  β,  θ. Then, we get

cos2α + cos2β + cos2θ = 1

Given that  \(\alpha=\cfrac{\pi}3\) and  \(\beta=\cfrac{\pi}2,\) we have to calculate θ

Hence,  \(\theta=\cfrac{\pi}6\)

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