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Anyone please correct me if I'm wrong but I think it's arbitrary which field points in which direction, and it's only done this way for convention. What matters is that the waves propagate at right angles to one another.
As other people have already said, the key takeaway is that Electric and Magnetic Fields are perpendicular, but if you wanted to learn more about why this is true you might want to look into Maxwell's Equations. I'm not sure if this course covers Maxwell, but you will learn it if you take the physics series.
The E-M fields are perpendicular to each other always while they oscillate. The electric field can oscillate up and down if the magnetic field oscillates right and left. These oscillations form the light wave.
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