Answer
$\alpha\approx68.2^\circ,\beta\approx56.1^\circ,\gamma\approx138.0^\circ$, $\vec v=\sqrt {29}(cos68.2^\circ i+cos56.1^\circ j+cos138.0^\circ k)$
Work Step by Step
1. Given $\vec v=2i-3j-4k$, we have $||\vec v||=\sqrt {4+9+16}=\sqrt {29}$
2. We have $\alpha=cos^{-1}(\frac{2}{\sqrt {29}})\approx68.2^\circ$
3. We have $\beta=cos^{-1}(\frac{3}{\sqrt {29}})\approx56.1^\circ$
4. We have $\gamma=cos^{-1}(\frac{-4}{\sqrt {29}})\approx138.0^\circ$
5. We have $\vec v=\sqrt {29}(cos68.2^\circ i+cos56.1^\circ j+cos138.0^\circ k)$
