How to get started on showing the conditions that $ax+by+cz=0$ I am looking at this question from Hardy's book, A Course of Pure Mathematics and have no idea where to begin.
I was wondering, what is the first step to deriving the conditions?
Question
What are the conditions that $ax+by+cz=0$ for all values of $x,y,z$?

It needs to be an identity which implies $a=0,b=0,c=0$
If it were anything other than $(0,0,0)$, then equation $ax+by+cz=0$ would represent a plane that doesn't cover all $x,y,z\in\Bbb R$
