The intersection of a plane and a surface in R3 is the set of points that lie on both the plane and the surface. It can be a line, a point, or even an empty set depending on the specific equations of the plane and surface.
To find the intersection of a plane and a surface in R3, you can solve the system of equations formed by the equations of the plane and surface. This will give you the coordinates of the points that lie on both the plane and surface, if they exist.
Yes, a plane and a surface in R3 can intersect at more than one point. This can happen if the plane and surface are not parallel and their equations have multiple solutions when solved together.
Yes, it is possible for a plane and a surface in R3 to have no intersection. This can happen if the plane and surface are parallel and their equations have no solutions when solved together.
The intersection of a plane and a surface in R3 is a 3D representation of the solution set of the system of equations formed by the plane and surface. It is a way to visualize the points in 3D space that satisfy both equations simultaneously.