CAD tip # 9357:

When you have got a simple 3D line and a 3D face, you can use the ilp function in AutoCAD geometric calculator - see Tip 4201.

For more complex cases, use an auxiliar construction with projected curve on the given plane or surface.

1. If the plane is defined by a 3DFACE, convert it to a region using the REGION command. If the surface is defined by a 3D mesh or similar object, convert it first to a surface with CONVTOSURFACE.
2. Switch to a user coordinate system (UCS) defined by the surface plane - on curved surfaces use an approximate projection near the expected intersection point. See e.g. the command UCS with the option obJect.
3. Use the PROJECTGEOMETRY command to project the 3D line (polyline, curve) onto the selected surface. If needed, select the view/project direction: "Ucs".
4. Now the 3D intersection of the original and the projected curves is the requested intersection point - you can use it to create a point (POINT), get its coordinates (ID), etc. - use the osnap INTerstection to acquire exact coordinates.