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]

Vector Calculus on Google Books (http://books.google.ca/books?id=9wmR7kDdO8EC&pg=PA51&lpg=PA51&dq=directional+derivative+scalar+field&source=bl&ots=BVaqINzgRV&sig=ONZdk_UhOsqcj0V9U0vEUiBaSgI&hl=en&ei=Em3vSpaSMtGTlAezt6n_BA&sa=X&oi=book_result&ct=result&resnum=4&ved=0CBQQ6AEwAzgK#v=onepage&q=directional%20derivative%20scalar%20field&f=false)

Directional Derivative on Physcisforums (http://www.physicsforums.com/library.php?do=view_item&itemid=82)

Notes from University of Edinburgh (http://www2.ph.ed.ac.uk/~rhorsley/SII08-09_mp2a/lec14_2.pdf)

[mudkip9001]

Vector Calculus on Google Books (http://books.google.ca/books?id=9wmR7kDdO8EC&pg=PA51&lpg=PA51&dq=directional+derivative+scalar+field&source=bl&ots=BVaqINzgRV&sig=ONZdk_UhOsqcj0V9U0vEUiBaSgI&hl=en&ei=Em3vSpaSMtGTlAezt6n_BA&sa=X&oi=book_result&ct=result&resnum=4&ved=0CBQQ6AEwAzgK#v=onepage&q=directional%20derivative%20scalar%20field&f=false)

Directional Derivative on Physcisforums (http://www.physicsforums.com/library.php?do=view_item&itemid=82)

Notes from University of Edinburgh (http://www2.ph.ed.ac.uk/~rhorsley/SII08-09_mp2a/lec14_2.pdf)

perfect, thank you again.