做条辅助线哈:设AC边中点为D,连接OD
因为:OA+OC=2OD,故:2OD=-3OB,即:OD=-3OB/2
说明OD和OB是共线向量,即BD是AC边的中线,且:
|OD|=3|BD|/5,故:S△AOC=3S△ABC/5.而:S△AOD=S△COD
且:S△AOD=3S△ABD/5,故:S△AOB=S△ABC/2-S△AOD=S△ABC/2-S△AOC/2
S△ABC/2-3S△ABC/10=S△ABC/5,故:S△AOB/S△AOC=(1/5)/(3/5)=1/3
做条辅助线哈:设AC边中点为D,连接OD
因为:OA+OC=2OD,故:2OD=-3OB,即:OD=-3OB/2
说明OD和OB是共线向量,即BD是AC边的中线,且:
|OD|=3|BD|/5,故:S△AOC=3S△ABC/5.而:S△AOD=S△COD
且:S△AOD=3S△ABD/5,故:S△AOB=S△ABC/2-S△AOD=S△ABC/2-S△AOC/2
S△ABC/2-3S△ABC/10=S△ABC/5,故:S△AOB/S△AOC=(1/5)/(3/5)=1/3