|向量a|=2,|向量b|=1，两者夹角为:派/3，求向量2a+3b与3a-b的夹角

由于a、b夹角为 π/3，可以不失一般性的假设 a = 2[cos(π/3) + i*sin(π/3)] = 1 + √3*i b = 1 A = 2a + 3b = (2*1 + 3*1) + 2√3*i = 5 + 2√3*i 斜率：K1 = 2√3/5 B = 3a - b = (3 - 1) + √3*i = 2 + √3*i 斜率：K2 = √3/2 tg(B-A) = (K2 - K1)/(1