38. Calculate the angle between the bisectors of the coordinate angles $x O y$ and $y O z$.
38. The bisector of angle $x O y$ is defined by the vector $\vec{r}_{1}=\vec{i}+\vec{j}$; the bisector of angle $y O z$ is defined by the vector $\overrightarrow{r_{2}}=\vec{j}+\vec{k}$. Consider the scalar product: $\quad \vec{r}_{1} \cdot \vec{r}_{2}=(\vec{i}+\vec{j}) \cdot (\vec{j}+\vec{k})=1=$ $=r_{1} r_{2} \cos \varphi$. But $\left|r_{1}\right|=\left|r_{2}\right|=\sqrt{2}$.

$$
\text { Hence } \cos \varphi=\frac{1}{\sqrt{2} \cdot \sqrt{2}}=\frac{1}{2} ; \varphi=60^{\circ} \text {. }
$$