B

1103025301

Level: 
B
The base \( ABCD \) of a square pyramid \( ABCDV \) has an edge of \( 6\,\mathrm{cm} \). The height of the pyramid is \( 4\,\mathrm{cm} \). Find the distance between the point \( V \) and the line \( BC \).
\( 5\,\mathrm{cm} \)
\( \sqrt{52}\,\mathrm{cm} \)
\( 25\,\mathrm{cm} \)
\( \sqrt{10}\,\mathrm{cm} \)

1103021001

Level: 
B
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 \( \overrightarrow{v}\cdot\overrightarrow{u} \).
\( \overrightarrow{v}\cdot\overrightarrow{w}=9 \), \( \overrightarrow{v}\cdot\overrightarrow{z} = 0 \), \( \overrightarrow{v}\cdot\overrightarrow{u}=27 \)
\( \overrightarrow{v}\cdot\overrightarrow{w}=9 \), \( \overrightarrow{v}\cdot\overrightarrow{z} = 0 \), \( \overrightarrow{v}\cdot\overrightarrow{u}=9\sqrt6 \)
\( \overrightarrow{v}\cdot\overrightarrow{w}=\frac92 \), \( \overrightarrow{v}\cdot\overrightarrow{z} = 0 \), \( \overrightarrow{v}\cdot\overrightarrow{u}=9\sqrt6 \)
\( \overrightarrow{v}\cdot\overrightarrow{w}=\frac92 \), \( \overrightarrow{v}\cdot\overrightarrow{z} = 1 \), \( \overrightarrow{v}\cdot\overrightarrow{u}=27 \)