What is the difference between the gradient vector at a point on a surface and the normal vector of the tangent plane at the same point on the surface?

Question

anonymous · Answer

as far as I can work out it seems that the gradient and the normal of a tangent plane at the same point are the same thing? In my textbooks it states that gradient f = <fx,fy,fz> and the way to figure out the normal vector of a tangent plane at the same point is the same? I'm a little confused and may have misread this. Could you clarify this a little?

anonymous · Answer

they are actually parallel to each other. sorry for any confusion my previous deleted statement may have arose

anonymous · Answer

As they are parallel, the process of calculating the both of them should be the same, is that right?

anonymous · Answer

yes. the only "difference" i'd say is that the gradient is obtained from the surface function and the normal vector is obtained from the tangent plane to the surface.

in other words, you can't find the gradient of a plane [plane being a flat surface]

anonymous · Answer

the first sentence should end with "at a given point"

anonymous · Answer

That helps a lot. Thanks for your help!

anonymous · Answer

glad i could help :)