摘要
b<sup>2</sup>=|b|<sup>2</sup>=（2n-3m）<sup>2</sup>=9m<sup>2</sup>-12m·n+4n<sup>2</sup>=9-12×1/2+4=7,∴|a|=7<sup>1/2</sup>,|b|=7<sup>1/2</sup>.又∵a·b（2m+n）·（2n-3m）=-6m<sup>2</sup>+m·n+2n<sup>2</sup>=-6+1/2+2=-31/2,∴cos〈a,b〉=（a·b）/（|a||b|）=（-31/2）/(7<sup>1/2</sup>×7<sup>1/2</sup>)=-1/2,∴向量a与向量b所成的角为120°.
