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b~2=|b|~2=(2n-3m)~2=9m~2-12m·n+4n~2=9-12×1/2+4=7,∴|a|=7~(1/2),|b|=7~(1/2).又∵a·b(2m+n)·(2n-3m)=-6m~2+m·n+2n~2=-6+1/2+2=-31/2,∴cos〈a,b〉=(a·b)/(|a||b|)=(-31/2)/(7~(1/2)×7~(1/2))=-1/2,∴向量a与向量b所成的角为120°.
b~2=|b|~2=(2n-3m)~2=9m~2-12m·n+4n~2=9-12×1/2+4=7, ∴|a|=7~( 1/2),|b|=7~(1/2). Also ∵a·b(2m+n)·(2n-3m)=-6m~2+m·n+2n~2=-6+ 1/2+2=-31/2, ∴cos=(a·b)/(|a||b|)=(-31/2)/(7 to (1/2) × 7~(1/2))=-1/2, the angle between the vector a and the vector b is 120°.