Number of points reduced in projection

Question

Several points in space are projected orthogonally on some three planes $\alpha$, $\beta$ and $\gamma$. Could it happen that in the three projections, plane $\alpha$ contains 3 points, plane $\beta$ contains 7 points, and plane $\gamma$ contains 10 points?

Answer 1

Yes, consider $$(1,1,0), (1,2,0), (1,3,0), (1,4,0), (1,5,0), (1,6,0), (1,7,0), (2,1,0), (3,1,0), (2,2,0)$$ and projections to the standard coordinate planes.