If a unit vector \( \vec{a} \) makes angles \( \frac{\pi}{3} \) wit...

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If a unit vector \( \vec{a} \) makes angles \( \frac{\pi}{3} \) with \( \hat{i}, \frac{\pi}{4} \) with \( \hat{j} \) and an acute angle \( \theta \) with
P \( \hat{k} \), then find \( \theta \) and hence, the components of \( \vec{a} \).

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