设A（x1,y1）,B（x2,y2）,
向量OA点乘向量OB等于1,则有x1x2+y1y2=1=x1x2+(kx1+√2)(kx2+√2)
=(1+k^2)x1x2+√2k(x1+x2)+2,
将y=kx+√2代入椭圆方程,x^2/3+(kx+√2）^2=1,
即(3k^2+1)x^2+6√2kx+3=0,
x1,x2是方程的根,则
x1+x2=-6√2k/(3k^2+1),x1x2=3/(3k^2+1),
将它们代入1=(1+k^2)x1x2+√2k(x1+x2)+2,
化简有(4-6k^2)/(3k^2+1)=0解得k=√6/3或-√6/3