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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!

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  • $\begingroup$ Obviously $(0,0,0)$ and $(1,1,1)$ are solutions, hence the line determined by these points. $\endgroup$ – Michael Hoppe Feb 14 at 14:57
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Yes, this is correct and it is the simplest way to prove what you want.

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