Gradient vectors

[KindofSlow]

Hello,
I'm working gradient vector problems in 3-D space.
Are the terms "tangent plane" and "level surface" synonymous?

Thank you

 

[Deleted member 4993]

Hello,
I'm working gradient vector problems in 3-D space.
Are the terms "tangent plane" and "level surface" synonymous?

Thank you

Those are NOT synonymous terms.

However a tangent plane has the property of being level surface (adjective).

Level surface means a surface with curvature = 0 (radius of curvature = infinity).

Definition of tangent plane is that a plane which intersects a curved plane only at one point (within a small region).