Points and vectors

2010015704

Level: 
A
Given the vectors \( \overrightarrow{a} \), \( \overrightarrow{b} \), and \( \overrightarrow{c} \) shown in the picture, express the vector \( \overrightarrow{c} \) as a linear combination of vectors \( \overrightarrow{a} \) and \( \overrightarrow{b} \).
\( \overrightarrow{c} = -\overrightarrow{a}-2\overrightarrow{b} \)
\( \overrightarrow{c} = -\overrightarrow{a} + \frac12 \overrightarrow{b} \)
\( \overrightarrow{c} = -2\overrightarrow{a} - \overrightarrow{b} \)
\( \overrightarrow{c} = 2\overrightarrow{a} + \frac32 \overrightarrow{b} \)

2010015703

Level: 
A
The picture shows a rectangular cuboid \( ABCDEFGH \). In the cuboid find the vector that is the sum of \( \overrightarrow{AB} + \overrightarrow{AH} + \overrightarrow{EG} + \overrightarrow{FA} + \overrightarrow{HE} \).
\( \overrightarrow{AC} \)
\( \overrightarrow{FH} \)
\( \overrightarrow{AG} \)
\( \overrightarrow{BH} \)