Giải bài 7 trang 28 – SGK Hình học lớp 10
Cho sáu điểm \(M,N,P,Q,R,S\) bất kì. Chứng minh rằng
\(\overrightarrow{MP} +\overrightarrow{NQ} +\overrightarrow{RS} =\overrightarrow{MS} +\overrightarrow{NP} +\overrightarrow{RQ} \)
Áp dụng qui tắc ba điểm, ta có:
\(\overrightarrow{MP} +\overrightarrow{NQ} +\overrightarrow{RS} =\overrightarrow{MS} +\overrightarrow{SP} +\overrightarrow{NP}+\overrightarrow{PQ}+\overrightarrow{RQ}+\overrightarrow{QS} \\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,=\left(\overrightarrow{MS} +\overrightarrow{NP} +\overrightarrow{RQ}\right)+\left(\overrightarrow{SP} +\overrightarrow{PQ} +\overrightarrow{QS}\right)\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,=\left(\overrightarrow{MS} +\overrightarrow{NP} +\overrightarrow{RQ}\right)+\overrightarrow{0}\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,=\overrightarrow{MS} +\overrightarrow{NP} +\overrightarrow{RQ}\)
Ghi nhớ:
Quy tắc ba điểm: \(\overrightarrow {AB}+\overrightarrow {BC}=\overrightarrow {AC}\)
