14. $\overrightarrow{O A} 、 \overrightarrow{O B}$ are both unit vectors, $\overrightarrow{O A}=\{p, q, 0\}, \overrightarrow{O B}=\{r, s, 0\}$, and both form a $45^{\circ}$ angle with $\overrightarrow{O C}=$ $\{1,1,1\}$.
(1) Find the values of $p+q$ and $p q$; (2) Find the size of $\angle A O B$ (acute angle).
14. (1) $|\overrightarrow{O A}|=1$, i.e., $p^{2}+q^{2}=1,|\overrightarrow{O C}|=\sqrt{3}$. Also, $\overrightarrow{O A}$ and $\overrightarrow{O C}$ form a $45^{\circ}$ angle, so $p+q=1 \cdot \sqrt{3} \cdot \cos 45^{\circ}$, thus $p+q=\frac{\sqrt{6}}{2}, p q=\frac{1}{4}$;
(2) $\cos \theta=\frac{\overrightarrow{O A} \cdot \overrightarrow{O B}}{|\overrightarrow{O A}||\overrightarrow{O B}|}=p r+q s=\frac{1}{4}+\frac{1}{4}=\frac{1}{2} \cdot \angle A O B=60^{\circ}$.