§ 2

A parallelogram $O A B C$ is given. In it $\left|\overrightarrow {O A}\right|=2,\left|\overrightarrow {O C}\right|=3$, the angle $A O C$ is equal to $\pi / 3$. Find the coordinates of the point $B$ in the coordinate system $O, \overrightarrow {O C}, \overrightarrow {O A}$.

Three points $A\left(x_{1}, y_{1}\right), B\left(x_{2}, y_{2}\right), C\left(x_{3}, y_{3}\right)$ are given. Find the coordinates of the vertex $D$ of the parallelogram $A B C D$.

Draw in the plane the sets of points whose polar coordinates are related by the relations

Let $O, l, \mathbf{n}$ be a spherical coordinate system. Let us introduce a Cartesian rectangular coordinate system $O, \mathbf{e}_{1}, \mathbf{e}_{2}, \mathbf{n}$, where $\mathbf{e}_{1}$ is directed along $l$, and the angle $\pi / 2$ from $\mathbf{e}_{1}$ to $\mathbf{e}_{2}$ is measured in the direction of increase of the polar angle. Write the formulas expressing the Cartesian coordinates in terms of the spherical ones.

Fig. 2