Gradient of a scalar field in a given direction

[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.

 

[VeeEight]

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

 

[mudkip9001]

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

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?

 

[VeeEight]

http://books.google.ca/books?id=9wm...=directional derivative scalar field&f=false"

https://www.physicsforums.com/library.php?do=view_item&itemid=82"

http://www2.ph.ed.ac.uk/~rhorsley/SII08-09_mp2a/lec14_2.pdf"

 

[mudkip9001]

http://books.google.ca/books?id=9wm...=directional derivative scalar field&f=false"

https://www.physicsforums.com/library.php?do=view_item&itemid=82"

http://www2.ph.ed.ac.uk/~rhorsley/SII08-09_mp2a/lec14_2.pdf"

perfect, thank you again.