33. Write the scalar product of vectors $\overrightarrow{r_{1}}\left(x_{1} ; y_{1}\right)$ and $\overrightarrow{r_{2}}\left(x_{2} ; y_{2}\right)$ in coordinates.
33. Let $\vec{r}_{1}=x_{1} \vec{i}+y_{1} \vec{j} ; \overrightarrow{r_{2}}=x_{2} \vec{i}+y_{2} \vec{j}$. Since $\vec{i}^{2}=\overrightarrow{j^{2}}=1$, $\vec{i}:=0$, multiplying $\vec{r}_{1}$ and $\vec{r}_{2}$, we get:

$$
\vec{r}_{1} \vec{r}_{2}=x_{1} x_{2}+y_{1} y_{2}
$$

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