Recent content by DFeng25

Thank you very much! Those were the answers I needed, sorry it took so long for me to correctly phrase my initial question.

Would all of this be the same if the particle is moving along a parametric surface in ℝ3 defined by r(x,y)= <x,y,f(x,y)> I thought that n=\frac{\partial r}{\partial x} \times \frac{\partial r}{\partial y} And the partial derivatives represent the x- and y-components of the velocity vector...

Oops, I meant the normal to the tangent plane. Sorry about that.

Thank you. So just to clarify, the normal and velocity vectors are always perpendicular, but the gradient and normal vectors are not necessarily the same?

Hello. I can't seem to wrap my head around the geometry of the gradient vector in ℝ3 So for F=f(x(t),y(t)), \frac{dF}{dt}=\frac{dF}{dx}\frac{dx}{dt}+\frac{dF}{dy}\frac{dy}{dt} This just boils down to \frac{dF}{dt}=∇F \cdot v Along a level set, the dot product of the gradient vector and...