The RhinoCommon line, vector and plane structs provides all you’d need For instance, you could go:
myLine.Direction.IsParallelTo(myPlane.XAxis)
See this documentation.
https://developer.rhino3d.com/api/rhinocommon/rhino.geometry.line/direction
https://developer.rhino3d.com/api/rhinocommon/rhino.geometry.vector3d/isparallelto
https://developer.rhino3d.com/api/rhinocommon/rhino.geometry.plane/xaxis