Stars form from clouds of gas and dust. As they form they start to spin, as clumps of matter hit them. As they get bigger their gravity starts to affect the dust cloud around them, and begins to spin it into a disc shape. This is called an accretion disk.
So you have a big spinning disk of dust with a star at the middle. The rest of the planets form from this spinning disc, hence they’re all in the same plane.
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