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The planets in our solar system all orbit on the same plane because they all formed from the same dust cloud that was rotating in the same plane.

Indeed. And to elaborate: the random collisions which flattened the solar system (or galaxy) over billions of years all conserved angular momentum.

Minute Physics have a nice video on this: https://youtube.com/watch?v=tmNXKqeUtJM

Nice video, thanks for sharing.

And just to clarify to GP, the original dust was not in the same plane and the video explains why it ends up in the same plane.