Grad Vector Direction: Clarified with Grad F Surfaces

[seshikanth]

As we know grad F (F surface) is in normal direction. But we also have (grad F(r)) x r = F'(r) (r) x r = 0
this implies grad F is in direction of r i.e., radial direction. Radial and normal directions need not be same. Can any öne clarify THE DIRECTION OF GRAD VECTOR?
Thanks,

 

[seshikanth]

Can u please throw some light on this?
Thanks

 

[arildno]

For a level surface defined by F(r)=some constant, where "r" is the radial variable, then by necessity, those level surface(s) will be circles (in 2-D).
And therefore, the radial direction will always be parallell to the vector normal to the level surface.