Question

Fie un paralelogram ABCD. Demonstrati ca vectorul AC × vectorul BD= AD^2× AB^2.

Answer 1

Avem $\overrightarrow{AC}=\overrightarrow{AB}+\overrightarrow{AD}$
$\overrightarrow{BD}=\overrightarrow{AD}-\overrightarrow{AB}$
Atunci $\overrightarrow{AC}\cdot\overrightarrow{BD}=\overrightarrow{AD}^2-\overrightarrow{AB}^2=AD^2-AB^2$