I am looking a proof for next thing:
If M is a plane that passing through the axis so there are a,b,c who belonging to R, so that:
M={(x,y,z)in R^3 | ax+by+cz=0}
מממ...אני מכיר את השאלה הזאת מתרגיל באלגברה לינארית מהאוניברסיטה העברית
This is plane analytic geometry: there exists a normal vector (a,b,c) to the plane "tailed" or "kashur" to the origin in $\displaystyle \mathbb{R}^3$, and thus it has the formal above: scalar product $\displaystyle (a,b,c)\cdot (x,y,z)=0\Longrightarrow ax+by+cz=0$.
Of course, the above depends on how you've defined a plane in space...
Tonio