以C为原点,CB方向为x轴的正向建立坐标系,将A放在第一象限,则C (0,0),
设A(m,n),B(b,0),O(x,y),(m,n,b均为正数),从而
OA向量=(m-x,n-y),OB向量=(b-x,-y),OC向量=(-x,-y),代入2OA向量+3OB向量+5OC向量=0向量,得
2(m-x,n-y)+3(b-x,-y)+5(-x,-y)=0
2(n-y)+3(-y)+5(-y)=0
y=n/5
S=(1/2)bn
S1=(1/2)by=(1/2)b(n/5)= (1/10)bn
两式相除得S1/S=1/5,所以x=1/5