Question

已知向量a=(1,2),b=(cosα,sinα),设向量m=向量a+t向量b（t为实数）,

Answer 1

a⊥b则a*b＝0

|a-b|^2＝(a-b)*(a-b)＝|a|^2+|b|^2＝5+1＝6|a-b|＝√6

|a+tb|^2＝(a+tb)*(a+tb)＝|a|^2+t^2×|b|^2＝5+t^2|a+tb|＝√(5+t^2)

(a-b)*m＝(a-b)*(a+tb)＝|a|^2-t|b|^2＝5-t

a-b与m夹角π/4则cos(π/4)＝[(a-b)*(a+tb)]/|a-b|*|a+tb|]＝(5-t)/[√6*(5+t^2)t＝(-5±3√5)/2