Question

已知在三角形ABC中,向量AB*向量BC=3,记为θ

Answer 1

(1)AB*BCcosθ=3

S=0.5AB*BC*sinθ

2S=AB*BC*sinθ=3tanθ

√3≤2S≤3

√3/3≤tanθ≤1

π/6≤θ≤π/4

(2)cacos(π/3)=0.5ac=3

ac=6

cos(2π/3)=(a^2+c^2-b^2)/2ac=-1/2

b^2=a^2+c^2+ac>=2ac+ac=3ac=18 a=c=√6时取等号

b>=3√2

最小值为3√2