Question

单位向量e1.e2的夹角为60度求向量a=e1+e2,b=e2-2e1的夹角

Answer 1

e1*e2＝|e1|×|e2|×cos60°＝1/2

|a|^2＝(e1+e2)*(e1+e2)＝|e1|^2＋|e2|^2＋2e1*e2＝3,|a|＝√3

|b|^2＝(e2-2e1)*(e2-2e1)＝|e2|^2＋4|e1|^2－4e1*e2＝3,|b|＝√3

a*b＝(e1+e2)*(e2－2e1)＝－2|e1|^2＋|e2|^2－e1*e2＝－3/2

a与b的夹角θ的余弦cosθ＝(a*b)/(|a|*|b|)＝－1/2,所以θ＝120°