Answer
$\alpha\approx60.9^\circ,\beta\approx144.2^\circ,\gamma\approx71.1^\circ$, $\vec v=\sqrt {38}(cos60.9^\circ i+cos144.2^\circ j+cos71.1^\circ k)$
Work Step by Step
1. Given $\vec v=3i-5j+2k$, we have $||\vec v||=\sqrt {9+25+4}=\sqrt {38}$
2. We have $\alpha=cos^{-1}(\frac{3}{\sqrt {38}})\approx60.9^\circ$
3. We have $\beta=cos^{-1}(\frac{-5}{\sqrt {38}})\approx144.2^\circ$
4. We have $\gamma=cos^{-1}(\frac{2}{\sqrt {38}})\approx71.1^\circ$
5. We have $\vec v=\sqrt {38}(cos60.9^\circ i+cos144.2^\circ j+cos71.1^\circ k)$
