$\underset{AB}{\rightarrow}$.$\underset{AC}{\rightarrow}$ = AB.AC.cos(\underset{AB}{\rightarrow},\underset{Ac}{\rightarrow})=4.5.cos120° =-10
Ta lại có: $\underset{AM}{\rightarrow}$ = $\frac{1}{2}$($\underset{AB}{\rightarrow}$+$\underset{AC}{\rightarrow}$)
và $\underset{BD}{\rightarrow}$ = $\underset{BA}{\rightarrow}$ +$\underset{AD}{\rightarrow}$
=-$\underset{AB}{\rightarrow}$ + $\frac{2}{5}$($\underset{AC}{\rightarrow}$
=> $\underset{AM}{\rightarrow}$.$\underset{BD}{\rightarrow}$
= $\frac{1}{2}$. $4^{2}$ + $\frac{}{5}$. (-10) - $\frac{1}{2}$.(-10)+$\frac{1}{5}$.$5^{2}$ = 0
Suy ra AM vuông góc BD.
Vậy $\underset{AB}{\rightarrow}$. $\underset{AC}{\rightarrow}$= -10 và AM vuông góc BD