Question

向量及其应用.已知a向量,b向量 是两个给定的向量,它们的夹角为θ,向量c=a向量+tb向量（t∈R）.求c向量的模的最

Answer 1

c=a+tb

|c|^2 = (a+tb).(a+tb)

= |a|^2+t^2|b|^2+ 2t|a||b|cosθ

d(|c|^2)/dt = 2t|b|^2 +2|a||b|cosθ = 0

t =-|a|cosθ/ |b|

(|c|^2)'' =2|b|^2 > 0 ( min)

min |c| when t = |a|cosθ/ |b|

=|a|sinθ

t = -|a|cosθ/ |b|

c = a -[ |a|cosθ/ |b|] b

c.b = (a -[ |a|cosθ/ |b|] b ).b

= a.b - |a||b|cosθ =0

b,c的夹角 = π/2