## Let $a$ and $b$ be unit vectors inclined at an variable angle $θ(θϵ(0,2π )(2π ,π)).$

Let $g(θ)=∫_{−(a.b)_{2}}f_{2}(x)dx+∫_{λ}f_{2}(x)dx−λ2 ,whereλ>0,$is function satisfying $f(x)+f(y)=xyx+y ,x,yϵR−[0]andh(θ)=−g(θ)+∣a×b∣_{2}.(a.b_{1})_{2},b_{1}=2b$

If $∣g(θ)∣$ is attaining its minimum value, then minimum distance between origin and the point of intersection of lines $r×a=a×b$ and $r×b=b×a$ is