Prove that if $\mathbf{u}$ and $\mathbf{v}$ are nonzero orthogonal vectors in $\Bbb R^n$ they are linearly Independent.
I've struggled with this a bit, here is what I know so far:
Suppose $\mathbf{u}$ and $\mathbf{v}$ are orthogonal. Then $\mathbf{u\cdot v}=0$ and $c_1\mathbf{u}+c_2\mathbf{v}=0$ is linearly Independent iff $c_1=c_2=0$
I know I need to end with $c_1=c_2=0$ but I can't find a path that reaches this conclusion. I feel like I need to use properties of the dot product to connect my first assumption to my second assumption but I'm lost on the way.