Is the Gradient Vector Always in the Radial Direction?

[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?

 

[seshikanth]

Gentle reminder

 

[HallsofIvy]

In your second formula, you refer to "F(r)" so you are assuming that F depends only on r and so is spherically symmetric. The first formula does not assume that .

 

[seshikanth]

Got it! Thanks!