5.10. Given vectors $\bar{a}(6 ;-8 ; 5 \sqrt{2})$ and $\bar{b}(2 ;-4 ; \sqrt{2})$. Find the angle formed by the vector $\bar{a}-\bar{b}$ with the $O z$ axis.
5.10. The vector $\bar{a}-\bar{b}$ has coordinates $(4; -4; 4 \sqrt{2})$. Let $\bar{k}(0; 0; 1)$ be the unit vector directed along the $O z$ axis. Assuming $(\widehat{a}-\bar{b}; \bar{k})=\gamma$, we find

$$
\cos \gamma=\frac{(\bar{a}-\bar{b}) \bar{k}}{|\bar{a}-\bar{b}||\bar{k}|}=\frac{4 \sqrt{2}}{\sqrt{16+16+32 \cdot 1}}=\frac{\sqrt{2}}{2}, \text{ i.e. } \gamma=45^{\circ}
$$

Answer: $45^{\circ}$.