设$\stackrel{\rightharpoonup }{a}:\stackrel{\rightharpoonup }{b}$为非零向量，$\left|\stackrel{\rightharpoonup }{b}\right|=2\left|\stackrel{\rightharpoonup }{a}\right|$，两组向量$\stackrel{\rightharpoonup }{x_1}:\stackrel{\rightharpoonup }{x_2}:\stackrel{\rightharpoonup }{x_3}:\stackrel{\rightharpoonup }{x_4}$和$\stackrel{\rightharpoonup }{y_1}:\stackrel{\rightharpoonup }{y_2}:\stackrel{\rightharpoonup }{y_3}:\stackrel{\rightharpoonup }{y_4}$均由2个$\stackrel{\rightharpoonup }{a}$和2个$\stackrel{\rightharpoonup }{b}$排列而成，若$\stackrel{\rightharpoonup }{x_1}·\stackrel{\rightharpoonup }{y_1}+\stackrel{\rightharpoonup }{x_2}·\stackrel{\rightharpoonup }{y_2}+\stackrel{\rightharpoonup }{x_3}·\stackrel{\rightharpoonup }{y_3}+\stackrel{\rightharpoonup }{x_4}·\stackrel{\rightharpoonup }{y_4}$所有可能取值中的最小值为$4{\left|\stackrel{\rightharpoonup }{a}\right|}^2$，则$\stackrel{\rightharpoonup }{a}$与$\stackrel{\rightharpoonup }{b}$的夹角为（）

A．

$\frac{2}{3}\pi$

B．

$\frac{\pi }{3}$

C．

$\frac{\pi }{6}$

D．

$0$

科目 数学   题型 选择题   难度 中等