e=√6/3
设过焦点F2直线:y=x-c
与x^2/a^2+y^2=1联立
(1+a^2)x^2-2a^2cx+c^2a^2-a^2=0
设A(x1,y1),B(x2,y2)
向量OA+向量OB
=(x1+x2,y1+y2)
=(x1+x2,x1+x2-2c)
向量a(3,-1) 共线
∴3(x1+x2-2c)=-(x1+x2)
4(x1+x2)=6c
2(x1+x2)=3c
韦达定理
2(2a^2c)/(1+a^2)=3c
4a^2=3+3a^2
a^2=3
∴椭圆x^2/3+y^2=1
c^2=3-1=2
c=√2
e=√2/√3
=√6/3
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