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High school math winter vacation homework.
Solution: (1). Let a = (- 1, 0); b=(cos60,sin60 )=( 1/2,√3/2); c=(cos60,-sin60 )=( 1/2,-ì3/2);

So A-B = (-1-1/2,0-√ 3/2) = (-3/2,-√ 3/2);

So (a-b)? c=-3/4+3/4=0,∴(a-b)⊥c;

(2)ka+b+ c =(-k+ 1/2+ 1/2,0+√3/2-√3/2)=(-k+ 1,0);

So ∣ ka+b+c ∣ = ∣ (-k+ 1)? =∣-k+ 1∣>; 1,so-k+ 1 >; 1, that is, k

The value range of k is: K.