# Gradient of a scalar field in a given direction

1. Nov 2, 2009

### mudkip9001

I have to find the gradient of a scalar field, h, at a certain point in a direction given by a vector.

I know, $$\vec{\nabla}h$$ will give me the direction of maximum slope, and its magnitude is the magnitude of the slope, but i don't know where to start in finding the slope in any other direction. I've looked through my notes and all over the internet, with no luck.

Last edited: Nov 2, 2009
2. Nov 2, 2009

### VeeEight

Take the scalar product of $$\vec{\nabla}h$$ with a unit vector in the given direction.

3. Nov 2, 2009

### mudkip9001

thank you very much! I can't believe i couldn't find that anywhere. I'm happy to tke your word for it, but any chance you have a proof or reference of that for future referance?

4. Nov 2, 2009

### VeeEight

Last edited by a moderator: May 4, 2017
5. Nov 2, 2009

### mudkip9001

Last edited by a moderator: May 4, 2017