Answer
$\alpha\approx56.1^\circ$ $\beta\approx138^\circ$ $\gamma\approx68.2^\circ$
Work Step by Step
1. Given $\vec v=3i-4j+2k$, we have $||\vec v||=\sqrt {9+16+4}=\sqrt {29}$
2. Thus $\alpha=cos^{-1}(\frac{3}{\sqrt {29}})\approx56.1^\circ$
3. and $\beta=cos^{-1}(\frac{-4}{\sqrt {29}})\approx138^\circ$
4. finally $\gamma=cos^{-1}(\frac{2}{\sqrt {29}})\approx68.2^\circ$
