Question

Fie triunghiul ABC . Să se determine k ∈ℤ astfel încât AB(vector)+2BC(vector)+2CA(vector )=k•AB(vector )

Answer 1

   
[tex]\overrightarrow{BC}+\overrightarrow{CA}=\overrightarrow{AB}\\\\ 2\overrightarrow{BC}+2\overrightarrow{CA}=2\Big(\overrightarrow{BC}+\overrightarrow{CA}\Big)=2\overrightarrow{AB}\\\\ \overrightarrow{AB}+2\overrightarrow{BC}+2\overrightarrow{CA}=\overrightarrow{AB}+2\overrightarrow{AB}=\boxed{3\overrightarrow{AB}}\\\\ \boxed{k = 3} [/tex]