Answer
$\alpha,\approx54.7^\circ,\beta=\gamma\approx125.3^\circ$, $\vec v=\sqrt 3(cos54.7^\circ i+cos125.3^\circ j+cos125.3^\circ k)$
Work Step by Step
1. Given $\vec v=-i+j+k$, we have $||vec v||=\sqrt {1+1+1}=\sqrt 3$
2. We have $\alpha=cos^{-1}(\frac{\sqrt 3}{3})\approx54.7^\circ$
3. We have $\beta=cos^{-1}(\frac{-\sqrt 3}{3})\approx125.3^\circ$
4. We have $\gamma=cos^{-1}(\frac{-\sqrt 3}{3})\approx125.3^\circ$
5. We have $\vec v=\sqrt 3(cos54.7^\circ i+cos125.3^\circ j+cos125.3^\circ k)$
