在平面直角坐标系$xOy$中，已知向量$\stackrel{\rightharpoonup }{a},\stackrel{\rightharpoonup }{b},\left|\stackrel{\rightharpoonup }{a}\right|=\left|\stackrel{\rightharpoonup }{b}\right|=1,\stackrel{\rightharpoonup }{a}·\stackrel{\rightharpoonup }{b}=0$点$Q$满足$\stackrel{\rightharpoonup }{OQ}=\sqrt{2}(\stackrel{\rightharpoonup }{a}+\stackrel{\rightharpoonup }{b})$,$C=\left\{P\right|\stackrel{\rightharpoonup }{OP}=\stackrel{\rightharpoonup }{a}\cos \theta +\stackrel{\rightharpoonup }{b}\sin \theta ,0\le \theta \le 2\mathrm{\pi }\}$，区域$\Omega =\left\{P\right|0<r\le \left|\stackrel{\rightharpoonup }{PQ}\right|\le R,r<R\}$.若$C\cap \Omega$为两段分离的曲线，则

$1<r<R<3$ $1<r<R\le 3$ $r\le 1<R<3$ $1<r<3<R$