Suppose that a, b ∈ ℝ3 and a × b = 0 Prove that there exist scalars λ, μ at least one of

which is non-zero, such that $\displaystyle \lambda a= \mu b.$

Suppose we have λ, μ such that μ does not equal zero. And that a and b are vectors.

Using λa = μb we can re-arrange to get (λ/μ)a = b

Plugging this into a x b = 0, we get;

a x ( a(λ/μ)) = 0, re-arranging we get.

(a x a) (λ/μ) = 0

((a x a)/μ) = 0

Am i right so far? / Can any 1 show me the proof ?