Consider the planes: $$P1:x - y = 0$$ $$P2:y-z = 0$$ $$P3:-x+z = 0$$ Prove that the intersection of the planes is a line.
My solution:
Solving the system I've obtained that $x=y=z$ and I made the notation $x=t$. From here we get the parametric equations of a line $d$ and we can write the canonical form:
$$ d : {{x}\over1} = {{y}\over 1} = {{z}\over1} $$
Thus proving that the intersection of the 3 planes is a line. Is this correct? If so, are there any other ways to prove this? Thanks in advance!
Yes, this is correct and it is the simplest way to prove what you want.