Cho tam giác $\mathrm{ABC}$ có $\mathrm{N}$ thuộc cạnh $\mathrm{BC}$ sao cho $\mathrm{BN}=2 \mathrm{NC}$. Chứng minh \(\overrightarrow{A N}=\f...

Q: Cho tam giác $\mathrm{ABC}$ có $\mathrm{N}$ thuộc cạnh $\mathrm{BC}$ sao cho $\mathrm{BN}=2 \mathrm{NC}$. Chứng minh \(\overrightarrow{A N}=\f...

<figure class="image"><img alt="image.png" src="https://docdn.giainhanh.io/media/test/ae8af488d724a7d57c506f386a9d633e.png" srcset="https://docdn.giainhanh.io/media/test/eabde74911879fff4e5b7a985407700e.png 221w, https://docdn.giainhanh.io/media/test/ddc842ffb897df76a123fab3590179cc.png 500w" sizes="100vw" width="500"></figure>Ta có:$\overrightarrow{A N}=\overrightarrow{A B}+\overrightarrow{B N}=\overrightarrow{A B}+\frac{2}{3} \overrightarrow{B C}=\overrightarrow{A B}+\frac{2}{3}(\overrightarrow{B A}+\overrightarrow{A C})=\overrightarrow{A B}-\frac{2}{3} \overrightarrow{A B}+\frac{2}{3} \overrightarrow{A C}=\frac{1}{3} \overrightarrow{A B}+\frac{2}{3} \overrightarrow{A C}$

Question

Accepted Answer

Ta có:

$\overrightarrow{A N}=\overrightarrow{A B}+\overrightarrow{B N}=\overrightarrow{A B}+\frac{2}{3} \overrightarrow{B C}=\overrightarrow{A B}+\frac{2}{3}(\overrightarrow{B A}+\overrightarrow{A C})=\overrightarrow{A B}-\frac{2}{3} \overrightarrow{A B}+\frac{2}{3} \overrightarrow{A C}=\frac{1}{3} \overrightarrow{A B}+\frac{2}{3} \overrightarrow{A C}$

THPT Trần Nguyên Hãn - Đề thi giữa học kì 1 (CT) 20-21 - Tp. Hải Phòng - MĐ 5756