OpenLayers: Is it possible to set a projection to a VectorLayer (or VectorSource, or feature)

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I'm trying to add a client-generated vector shape to add to the map. I'm currently using a VectorLayer for this, with a VectorSource and some features added in it.

This vector shape may need to be positioned in specific locations in the map depending on what the user / application is doing. I am able to represent this location with respect to the map as a transformation between two projections: the map projection and a vector projection, but I can't for the life of me figure out how to set the projection used for the VectorLayer, it is always discarded.

Is there any way to specify the projection of a client-created VectorLayer? If so, how?

If not, what's the recommended approach to render a vector figure (which has specific relative points which make up this figure) in such a way that it's position and rotation can be specified and/or updated?

Thanks a lot for any guidance on this,

Julian

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