Is $xyz=0$ a joint variation

Question

Is $xyz=0$ a joint variation

I know that a joint variation is $\dfrac{x}{yz} = k$

I just want to know if $k$ is allowed to be zero

Answer 1

if $xyz=0 -----(1)$

$\implies x=0 $ or $y=0$ or $z=0$

and given that $\frac x{yz}=k----(2)$ and if $k=0$ implies

$x=0,y,z \ne 0$

Intersection of $(1)$ and $(2)$ with $k=0 $

implies $x=0$