已知向量a=(cosλθ,c0s(10-λ)θ),向量b=(sin(10-λ)θ,sinλθ),λ,θ∈R当θ=π/20时,求证：向量a平行向量b

Question

已知向量a=(cosλθ,c0s(10-λ)θ),向量b=(sin(10-λ)θ,sinλθ),λ,θ∈R
当θ=π/20时,求证：向量a平行向量b

Answer 1

已知a=(cosλθ,cos[(10-λ)θ])；b=(sin[(10-λ)θ],sinλθ)；λ,θ∈R,当θ=π/20时,求证a∥b.
当θ=π/20时,
a=(cos(λπ/20),cos[(10-λ)π/20])=(cos(λπ/20),cos(π/2-λπ/20))
=(cos(λπ/20),sin(λπ/20))；
b=(sin[(10-λ)π/20],sin(λπ/20))=(sin(π/2-λπ/20),sin(λπ/20))
=(cos(λπ/20),sin(λπ/20)).
故此时a=b,即a,b共线,当然也就有a∥b.