Equation of all planes passing through the given line?

Question

We are given a line $\overrightarrow r = \lambda(\hat i-\hat j+\hat k) $ which is the intersection of planes $ x+y=0$ and $y+z=0$.

How do I find the equation all planes passing through $ \overrightarrow r$ ?

Answer 1

$\alpha(x+y)+\beta(y+z)=0$, $\alpha,\beta\in\mathbb{R}$, $\alpha^2+\beta^2\ne0$