Question

cho tam giác ABC , lấy M,N,P lần lượt trên các đoạn AB,BC,AC sao cho AM= \(\frac{1}{3}\)AB, BN= \(\frac{1}{3}\) BC, CP= \(\frac{1}{3}\)CA. CMR: \(\overrightarrow{AN}+\overrightarrow{BP}+\overrightarrow{CM}=0\)

Answer 1

Có \(\overrightarrow{AN}=\overrightarrow{AB}+\overrightarrow{BN}\)

\(\overrightarrow{BP}=\overrightarrow{BC}+\overrightarrow{CP}\)

\(\overrightarrow{CM}=\overrightarrow{CA}+\overrightarrow{AM}\)

Cộng vế vs vế:

\(\overrightarrow{AN}+\overrightarrow{BP}+\overrightarrow{CM}=\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{CA}+\overrightarrow{BN}+\overrightarrow{CP}+\overrightarrow{AM}\)

\(=\overrightarrow{AC}+\overrightarrow{CA}+\frac{1}{3}\left(\overrightarrow{BC}+\overrightarrow{CA}+\overrightarrow{AB}\right)\)

\(=0+\frac{1}{3}\left(\overrightarrow{BA}+\overrightarrow{AB}\right)=0\) (đpcm)

Answer 2

xin slot để làm

Answer 3