...urface. Plz help I don't understand this difference. Thanks

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- Nov 1st 2012, 04:31 PMnicksbymanThe difference between a gradient vector to a surface and the normal vector to that s
...urface. Plz help I don't understand this difference. Thanks

- Nov 1st 2012, 05:48 PMchiroRe: The difference between a gradient vector to a surface and the normal vector to th
Hey nicksbyman.

If you have a definition, you should post it (if its from lectures notes or a book) but a gradient vector can refer to the tangential vector with respect to a particular variable (i.e. one based on the partial derivative of the surface at a particular point).

It's hard to say with certainty without knowing more information. - Nov 1st 2012, 07:05 PMHallsofIvyRe: The difference between a gradient vector to a surface and the normal vector to th
I think your problem is where you refer to the "gradient vector" of a

**surface**. There is no such thing. Rather, the gradient vector is the gradient of a**function**. If we have a function f(x,y,z) then the "gradient of f", also written $\displaystyle \nabla f$, is the "vector" $\displaystyle \frac{\partial f}{\partial x}\vec{i}+ \frac{\partial f}{\partial y}\vec{j}+ \frac{\partial f}{\partial z}\vec{k}$. Given such a function, the equation f(x,y,z)= constant, could, theoretically, be "solved" for one of the variables in terms of the other two. Since we can then have z= g(x,y), say, that equation defines a surface. Given the equation f(x,y,z)= C, $\displaystyle \nabla f$, the gradient vector of the**function**is a normal vector to the**surface**at every point.

(In Britain, the term "gradient" can be used to refer to the**derivative**of a function, which then is the slope of the tangent line. Chiro may be thinking of that situation. Why in the world can't those Brits speak**English**!)