1103021001

Let \( ABCDEF \) be a regular hexagon with the centre \( S \) and the side of length \( 3\,\mathrm{cm}\). The point \( G \) is the midpoint of the segment \( AB \). The vectors \( \overrightarrow{u} \), \( \overrightarrow{v} \), \( \overrightarrow{w} \), \( \overrightarrow{z} \) are indicated in the hexagon shown in the picture. Find the dot product of: \( \overrightarrow{v}\cdot\overrightarrow{w} \), \( \overrightarrow{v}\cdot\overrightarrow{z} \) and \( \overrightarrow{v}\cdot\overrightarrow{u} \).