Interactive 3d Scatter Plot and Planes

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I am trying to find some service/application/web-app or otherwise that allows for the following functionality:

  1. Plot points in 3d space
  2. Insert plane in 3d space wherever I like. As in it must not be the case that the only plane that can be inserted must be a regression plane that has been fit to the data. I should be able to insert the plane where ever I want, independent of the data points I have plotted.
  3. This 3d space should be interactive (rotatable and zoomable).
  4. I should be able to adjust the tilt of the plane in any direction.
  5. I should be able to see the residuals between the points and the plane.
  6. These residuals should be adjusting in real-time based on me interactively tilting the plane.

Points 1-3 are easily met with Geogebra (and I'm sure other applications). 4-6 is what I am struggling to find.

If this doesn't exist to your knowledge, do you know if there is some application I can use to create this.

Thank you.