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How can I generate a 3D plot with the orthographic projections of a parametric curve on the inside walls of the 3D plot, as shown in this youtube video?

I can generate a 3D plot of the curve using the plot3 function, but I cannot figure out how to create the blue orthographic projections on the inner walls of the cube or the red dashed lines:

enter image description here

Additionally, how could I generate and synchronize the 3 separate "Coordinate Functions" plots (not show on the diagram above but shown in the video)?

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