1103021001

SubArea: 
Points and Vectors
Level: 
B
Project ID: 
1103021001
Accepted: 
1
Clonable: 
0
Easy: 
0
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 \( \vec{u} \), \( \vec{v} \), \( \vec{w} \), \( \vec{z} \) are indicated in the hexagon shown in the picture. Find the dot product of: \( \vec{v}\cdot\vec{w} \), \( \vec{v}\cdot\vec{z} \) and \( \vec{v}\cdot\vec{u} \).
\( \vec{v}\cdot\vec{w}=9 \), \( \vec{v}\cdot\vec{z} = 0 \), \( \vec{v}\cdot\vec{u}=27 \)
\( \vec{v}\cdot\vec{w}=9 \), \( \vec{v}\cdot\vec{z} = 0 \), \( \vec{v}\cdot\vec{u}=9\sqrt6 \)
\( \vec{v}\cdot\vec{w}=\frac92 \), \( \vec{v}\cdot\vec{z} = 0 \), \( \vec{v}\cdot\vec{u}=9\sqrt6 \)
\( \vec{v}\cdot\vec{w}=\frac92 \), \( \vec{v}\cdot\vec{z} = 1 \), \( \vec{v}\cdot\vec{u}=27 \)