设m n是两个单位夹向量，其夹角为60度，求向量a=2m+n与b=2n-3m的夹角。

a与b的内积为mn+2n^2-6m^2=cos60度+2-6=-7/2
向量a的模平方为4m^2+4mn+n^2=4+2+1=7，向量b的模平方为4n^2-12mn+9m^2=4-6+9=7
所以a、b夹角余弦值为-1/2，夹角为120度。

|a|^2 = |2m+n|^2 = (2m+n)^2 = 4m^2+4mn +n^2 = 4*1 + 4*1*1*cos(60度) + 1 = 4 + 2 + 1 = 7
|b|^2 = |2n-3m|^2 = (2n-3m)^2 = 4n^2-12mn + 9m^2 = 4 - 6 + 9 = 7

所以|a|·|b| = 7
a·b = (2m+n)(2n-3m) = 4mn -6m^2 + 2n^2 -3mn = 2 - 6 + 2 - 3/2 = -7/2
所以cos(x) = a·b /(|a|·|b|) = -(7/2)/7 = -1/2
所以x = 120度