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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 acute angle θ with \(\hat{k}\) then find θ and hence, the component of \(\vec{a}\)

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\(\vec{a} = x\vec{i} + y\vec{j} + z\vec{k}\)

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