According to the known, x1* y1+x2 * y2+x3 * y3+x4 * y4 = a * (x1+x2)+b * (x3+x4),

There are only three possibilities: (1), = a * 2a+b * 2b = 2a2+2b2 =10a2;

(2)、= a *(a+b)+b *(a+b)= a^2+b^2+2a*b = 5a^2+2a * b；

(3)、= a*2b+b*2a = 4a*b .

Because |b|=2|a|, there is (1) >; (2)>(3),

So 4a * b = 4 | a | 2, then the cosine of the included angle between a and b is

Cosθ = a * b/(| a || b |) = a * b/(2 | a | 2) =1/2, so the included angle is 60 degrees.