Cho 6 điểm A, B, C, D, E, F. Chứng minh a) AB+ CD+ BC+ EA = ED b) AB+ BC+ CD+ FE+ DF= AE Giúp mik vs ạ 01/08/2021 Bởi Eliza Cho 6 điểm A, B, C, D, E, F. Chứng minh a) AB+ CD+ BC+ EA = ED b) AB+ BC+ CD+ FE+ DF= AE Giúp mik vs ạ
Giải thích các bước giải: $a) VT=\overrightarrow{AB}+\overrightarrow{CD}+\overrightarrow{BC}+\overrightarrow{EA}\\=\overrightarrow{EA}+\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{CD}\\=\overrightarrow{EB}+\overrightarrow{BC}+\overrightarrow{CD}\\=\overrightarrow{EC}+\overrightarrow{CD}\\=\overrightarrow{ED}=VP\Rightarrow ĐPCM$ $b) VT=\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{CD}+\overrightarrow{FE}+\overrightarrow{DF}\\=\overrightarrow{AC}+\overrightarrow{CD}+\overrightarrow{FE}+\overrightarrow{DF}\\=\overrightarrow{AD}+\overrightarrow{FE}+\overrightarrow{DF}\\=\overrightarrow{AD}+\overrightarrow{DF}+\overrightarrow{FE}\\=\overrightarrow{AF}+\overrightarrow{FE}\\=\overrightarrow{AE}=VP\Rightarrow ĐPCM$ Bình luận
TL:
Giải thích các bước giải:
$a) VT=\overrightarrow{AB}+\overrightarrow{CD}+\overrightarrow{BC}+\overrightarrow{EA}\\
=\overrightarrow{EA}+\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{CD}\\
=\overrightarrow{EB}+\overrightarrow{BC}+\overrightarrow{CD}\\
=\overrightarrow{EC}+\overrightarrow{CD}\\
=\overrightarrow{ED}=VP\Rightarrow ĐPCM$
$b) VT=\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{CD}+\overrightarrow{FE}+\overrightarrow{DF}\\
=\overrightarrow{AC}+\overrightarrow{CD}+\overrightarrow{FE}+\overrightarrow{DF}\\
=\overrightarrow{AD}+\overrightarrow{FE}+\overrightarrow{DF}\\
=\overrightarrow{AD}+\overrightarrow{DF}+\overrightarrow{FE}\\
=\overrightarrow{AF}+\overrightarrow{FE}\\
=\overrightarrow{AE}=VP\Rightarrow ĐPCM$