1. ## Vectors proof

I have got nowhere with this question: Non-zero non-parallel vectors a, b and c are such that b x c = c x a. Prove that a + b = kc for some scalar k.

2. ## Re: Vectors proof

Originally Posted by Stuck Man
I have got nowhere with this question: Non-zero non-parallel vectors a, b and c are such that b x c = c x a. Prove that a + b = kc for some scalar k.
By the given we know that $\vec{c}\times(\vec{b}\times \vec{c})=\vec{c}\times(\vec{c}\times \vec{a})$

But $\vec{c}\times(\vec{b}\times \vec{c})=(\vec{c}\cdot\vec{c})\vec{b}-(\vec{c}\cdot\vec{b})\vec{c}$

Now expand the RHS and solve for $\vec{a}+\vec{b}$.

3. ## Re: Vectors proof

I had not used the vector triple product before. I think I have done this now.