KnifeMissile

Tricky question...

I don't really know but if you assume that the constituent mass of the solar system had a consistent angular momentum (treating it as a vector, now), it makes sense that the solar system is on a plane.

The centrifugal "force" will keep the masses in orbit except that such a force can only exist on one plane. The normal orientation of that plane has no forces to keep the masses apart so the gravitational forces will pull them together.

In other words, in one dimension (the dimension normal to the plane of rotation), the masses attract each other and there's no force keeping them apart, so they come together, whereas, on the plane of rotation (the other two dimensions), while there is also gravitational attraction there, they have the centrifugal "force" to keep them apart and, thus, our solar system eventually forms a disc on this plane...