# Homework Help: Silly question

1. Aug 12, 2009

### seamonkeydoo

Just curious

Let's say I have a plane with the equation

4x + 5y + 6z = 45

If I find $$\nabla$$F(x,y,z) and then find it's magnitude, I get the direction of steepest descent/ascent in the direction of <$$\partial$$F(x,y,z)/$$\partial$$x,$$\partial$$F(x,y,z)/$$\partial$$y, $$\partial$$F(x,y,z)/$$\partial$$z> and the magnitude of the vector in that direction right?

How would I find the velocity vector of a particle from the top of the plane to the bottom in the direction of the gradient vector? Would I just think of it as an inclined plane? And how is velocity related to finding the gradient?

Last edited: Aug 12, 2009
2. Aug 12, 2009

### tiny-tim

Welcome to PF!

Hi seamonkeydoo! Welcome to PF!
uhh? It is an inclined plane!

Yes, the gradient vector "downhill" is the same as an actual vector "downhill".

Generally, the gradient vector of a curved surface is the same as the actual "downhill" vector of the tangent plane.
It'll be proportional to the gradient.