Gradient Vector for the Surface f(x,y,z)=0

PhysicStu · #1 $Old$ November 3rd, 2009, 11:58 AM

Please describe the Gradient Vector of the Surface f(x,y,z)=0 for me.

Thanks in advance...

Ruun · #2 $Old$ November 3rd, 2009, 02:54 PM

Given a function $f : \mathbb{R}^3 \to \mathbb{R}$ , $f \in C^{1}$ , the gradient of that function is a vector whose components in Cartesian coordinates are $\left(\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}, \frac{\partial f}{\partial z}\right)$ .

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