I have a problem and i can't find a solution. I have a face on my object. I want to align a vertice so that vertice is on the same plane of the face. I created a Trasform Orentation on the face so that i have the right axis where to move on the vertice. I also set the 3d cursor but when i want to put z=0 the vertices doesn't align with the face. I know that the problem is the local origin but i can't find any other method. I can move the vertices put all coordinates to 0 and restore x and y but it's a very dirty way.
If you want to snap all the vertices of the rim to the surface at once, you could assign them to a Vertex Group, temporarily P split the hatch off into a separate object, and give it a Shrinkwrap modifier, affecting only the vertex group, targeted on the surface.
If you align the hatch object-axes down the edge of interest,then you can use the modifier to project all the vertices in the desired direction. Apply the modifier, rejoin the objects.