This discussion revolves around finding a vector normal to a plane and a paraboloid at a specific point, (2,1,7). The subject area includes vector calculus and geometry related to planes and surfaces.
The discussion includes attempts to clarify the properties of normal vectors and their application to both the plane and the paraboloid. Some participants express uncertainty about the initial approach, while others suggest revisiting relevant concepts to find useful information.
Participants are navigating the specifics of the problem, including the definitions and properties of normal vectors in different contexts, as well as the implications of the given equations for the plane and paraboloid.
Dick said:A plane has the same normal everywhere, doesn't it?
mharten1 said:That's what I thought at first. But it seems too easy to be the solution to both questions. I'm going to read over the section again and see if I can find anything that will be useful.
Dick said:It's not the solution to the second question. Think about using the gradient.