If a unit vector makes angles frac{pi}{4} wit | vedclass

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(A) Let the unit vector be $\vec{u} = \cos \alpha \hat{i} + \cos \beta \hat{j} + \cos \gamma \hat{k}$.Given $\alpha = \frac{\pi}{4}$, $\beta = \frac{\

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$\frac{\pi}{3}$

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(A) Let the unit vector be $\vec{u} = \cos \alpha \hat{i} + \cos \beta \hat{j} + \cos \gamma \hat{k}$.Given $\alpha = \frac{\pi}{4}$, $\beta = \frac{\pi}{3}$, and $\gamma = 	heta$.The sum of the squares of the direction cosines is $\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1$.Substituting the values: $\cos^2(\frac{\pi}{4}) + \cos^2(\frac{\pi}{3}) + \cos^2 	heta = 1$.$(\frac{1}{\sqrt{2}})^2 + (\frac{1}{2})^2 + \cos^2 	heta = 1$.$\frac{1}{2} + \frac{1}{4} + \cos^2 	heta = 1$.$\frac{3}{4} + \cos^2 	heta = 1 \implies \cos^2 	heta = \frac{1}{4}$.$\cos 	heta = \pm \frac{1}{2}$.Since $	heta \in (0, \pi)$, $	heta = \frac{\pi}{3}$ or $	heta = \frac{2\pi}{3}$.

If a unit vector makes angles $\frac{\pi}{4}$ with $\hat{i}$, $\frac{\pi}{3}$ with $\hat{j}$ and $\theta \in (0, \pi)$ with $\hat{k}$, then a value of $\theta$ is equal to...

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