[Math] two orthogonal vectors that are not linearly indepdent

Question

I need to give an example of two orthogonal vectors that are not linearly independent.

My Workings:

I know that linear dependency of vectors $u$ and $v$ means that there exists number $a$ and $b$, which both cant be 0), such that $au+bv = 0 $. So $0=(au+bv)^T(au+bv) = a^2||u||^2+b||v||^2 $ because they are orthogonal. SO $ A\ne = 0$, then $u=0$. Thus, one of the vectors must be the zero vector.

Thus, would $(1,1)^T$ and $(0,0)^T$ be an example of two orthogonal vectors that are not linearly independent?

Answer 1

Yep! The vector 0 is orthogonal to all vectors and linearly dependent with all vectors.