(Solved): Find the direction angles of the given vector. Write the vector in terms of its magnitude and dire ...

Find the direction angles of the given vector. Write the vector in terms of its magnitude and direction cosines as \( v=\|v\|[(\cos \alpha) i+(\cos \beta) j+(\cos \gamma) k] \). \[ v=6 i+2 j-3 \mathbf{k} \] \( \alpha= \) degrees (Round to the nearest tenth of a degree, if necessary.) \( \beta= \) degrees (Round to the nearest tenth of a degree, if necessary.) \( \gamma= \) degrees (Round to the nearest tenth of a degree, if necessary.) (Simplify your answers. Type an exact value for \( \|\mathrm{v}\| \), using fractions and radicals as needed. Round each angle measure to the nearest tenth of a degree, if necessary.)