Cho tam giác abc . Tìm điểm M thỏa mãn:
a/ 3MA - 2MB + MC = 0
b/ 5MA - 2MB - MC = 0
Kẻ AF, BE là trung tuyến tam giác ABC
a,Ta có :
[tex]\underset{3MA}{\rightarrow}-\underset{2MB}{\rightarrow}+\underset{MC}{\rightarrow}=\underset{0}{\rightarrow}[/tex]
<=> [tex]\underset{MA}{\rightarrow}+\underset{MC}{\rightarrow}+\underset{2MA}{\rightarrow}-\underset{2MB}{\rightarrow}=\underset{0}{\rightarrow}[/tex]
<=>[tex]\underset{2ME}{\rightarrow}+\underset{2BA}{\rightarrow}=\underset{0}{\rightarrow}[/tex]
<=>[tex]\underset{ME}{\rightarrow}=\underset{AB}{\rightarrow}[/tex]
b,
[tex]\underset{5MA}{\rightarrow}-\underset{2MB}{\rightarrow}-\underset{MC}{\rightarrow}=\underset{0}{\rightarrow}[/tex]
<=>[tex]\underset{2BA}{\rightarrow}+\underset{CA}{\rightarrow}+\underset{2MA}{\rightarrow}=\underset{0}{\rightarrow}[/tex]
<=>................tương tự