Cho ΔABC. Gọi G là trọng tâm, D là điểm đối xứng của G qua B

 Chứng minh →DA−5→DB+→DC=→0

Câu hỏi này được treo giải thưởng trị giá +1000 vỏ sò bởi sheep9, đã hết hạn vào lúc 20-07-14 02:25 PM

Vì G là trọng tâm ΔABC ta có: →GA+→GB+→GC=→0
⇒→DG+→GA+→DG+→GB+→DG+→GC=3→DG
⇔→DA+→DB+→DC=3→DG
Vì D là điểm đối xứng của G qua B ta có: →DG=2→DB
Từ đó suy ra: →DA+→DB+→DC=6→DB
⇔→DA−5→DB+→DC=→0

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