A question in Do Carmo's differential geometry book states:
Given:
$$x^2+ y^2 + z^2 = ax$$ $$x^2+ y^2 + z^2 = by$$ $$x^2+ y^2 + z^2 = cz$$
The question is to show that those are regular surfaces (which is fairly straightfrward) But then it asks to show that they intersect orthogonally.
I am not sure what kind of quadrics (conicoids) are, but they are definitely not planes. What does it mean for a quadric (surface) to intersect "orthogonally"?