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题目(2014年安徽高考·理15)已知两个不相等的非零向量a,b,两组向量x_1,x_2,x_3,x_4,x_5和y_1,y_2,y_3,y_4,y_5均由2个a和3个b排列而成.记S=x_1·y_1+x_2·y_2+x_3·y_3+x_4·y_4+x_5·y_5,S_(min)表示S所有可能取值中的最小值,则下列命题正确的是_______(写出所有正确命题的编号).①S中有5个不同的值;②若a⊥b,则S_(min)与|a|无关;③若a∥b,则S_(min)与|b|无关;④若|b|>4|a|,则S_(min)>0;⑤若|b|=2|a|,S_(min)=8|a|~2,则a与b的夹角为π/4.
There are two non-zero nonzero vectors a and b that are known to each have two vectors x_1, x_2, x_3, x_4, x_5 and y_1, y_2, y_3, y_4 and y_5. a and b 3. S = x_1 · y_1 + x_2 · y_2 + x_3 · y_3 + x_4 · y_4 + x_5 · y_5, S_ (min) represents the smallest of all possible values of S. Then the following proposition Correct is _______ (write out the numbers of all the correct propositions). ① There are 5 different values in S; ② If a⊥b, S_ (min) has nothing to do with | a; ③ If a∥b, then S_ min) is independent of | b |, ④ if | b |> 4 | a |, then S_ (min)> 0; ⑤ If | b | = 2 | a |, S_ (min) = 8 | a | The angle between a and b is π / 4.