Část:
Project ID:
1103024303
Accepted:
1
Clonable:
0
Easy:
0
V kvádru \( ABCDEFGH \) na obrázku jsou vyznačeny vektory \( \overrightarrow{a} = \overrightarrow{AB} \), \( \overrightarrow{b} = \overrightarrow{AD} \), \( \overrightarrow{c} = \overrightarrow{AE} \), \( \overrightarrow{x} = \overrightarrow{AK} \) a \( \overrightarrow{y} = \overrightarrow{AL} \). Bod \( K \) je středem hrany \( FG \) a bod \( L \) je středem stěny \( BCGF \). Vyjádřete vektory \( \overrightarrow{x} \) a \( \overrightarrow{y} \) jako lineární kombinaci vektorů \( \overrightarrow{a} \), \( \overrightarrow{b} \), \( \overrightarrow{c} \).
\( \overrightarrow{x} = \overrightarrow{a} + \frac12\overrightarrow{b} + \overrightarrow{c};\ \overrightarrow{y} = \overrightarrow{a} + \frac12\overrightarrow{b} + \frac12\overrightarrow{c} \)
\( \overrightarrow{x} = \frac12\overrightarrow{a} + \overrightarrow{b} + \frac12\overrightarrow{c};\ \overrightarrow{y} = \overrightarrow{a} - \frac12\overrightarrow{b} + \frac12\overrightarrow{c} \)
\( \overrightarrow{x} = \overrightarrow{a} + \frac12\overrightarrow{b} + \frac12\overrightarrow{c};\ \overrightarrow{y} = \overrightarrow{a} - \frac12\overrightarrow{b} + \frac12\overrightarrow{c} \)
\( \overrightarrow{x} = \overrightarrow{a} + \frac12\overrightarrow{b} + \frac12\overrightarrow{c};\ \overrightarrow{y} = \frac12\overrightarrow{a} + \frac12\overrightarrow{b} + \frac12\overrightarrow{c} \)