Given two arbitrary equidistant points in $\mathbb{R}^3$, ($p$ and $q$), how would one show that they form a plane and what would the equation of that plane be?
Defining two vectors in $\mathbb{R}^3$: $(p - 0)$ and $(q - 0)$, the span of these two vectors show form a plane, if I'm not mistaken. But now, how can I come up with an equation for this plane?