Answer
$\alpha\approx115.4^\circ,\beta\approx31.0^\circ,\gamma\approx73.4^\circ,\\ \vec v=14(cos115.4^\circ i+cos31.0^\circ j+cos73.4^\circ k)$
Work Step by Step
1. Given $\vec v=-6i+12j+4k$, we have $||vec v||=\sqrt {36+144+16}=14$
2. We have $\alpha=cos^{-1}(\frac{-6}{14})\approx115.4^\circ$
3. We have $\beta=cos^{-1}(\frac{12}{14})\approx31.0^\circ$
4. We have $\gamma=cos^{-1}(\frac{4}{14})\approx73.4^\circ$
5. We have $\vec v=14(cos115.4^\circ i+cos31.0^\circ j+cos73.4^\circ k)$
