(Solved): Find the direction cosines and angles of \( \mathbf{u} \) and show that \( \cos ^{2} \alpha+\cos ^ ...

Find the direction cosines and angles of \( \mathbf{u} \) and show that \( \cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma=1 \). (Round your answers for the angles to four decimal places.) \[ \begin{array}{l} \mathbf{u}=-2 \mathbf{i}+5 \mathbf{j}+9 \mathbf{k} \\ \cos \alpha=\int \quad \Rightarrow \alpha \approx \quad \times \quad \mathrm{rad} \\ \cos \beta=\cos ^{-1} \frac{5}{\frac{110}{*}} \Rightarrow \beta \approx \quad \times \mathrm{rad} \\ \cos \gamma=\cos ^{-1} \frac{9}{=} \frac{\Rightarrow}{110} \quad \gamma \approx \mathrm{rad} \\ \end{array} \]