Question

I just finished finding the rate of change in the direction of a gradient at P, and want to find the rate of change in the direction of 45 degrees plus the gradient f(P). I tried adding pi/r to to 33i-4j, but the end result wasn't pretty. :P

Answer 1

Find a unit vector in the direction of the 45 degree line and take the dot product of the gradient with the unit vector.

Answer 2

Ok, I think I get it. \[\left| \left| a \right|\right|\left| \left| b \right| \right| \cos (\frac{\pi}{4}) \] is the left hand side?

Answer 3

I'll be back in a few. Gotta help the kids with something.

Answer 4

Yes, that is one way. Another way is to find the angle the gradient makes with the x-axis ( arctan(j_coefficient / i_coefficient) and then add 45 degrees to it and come up with a unit vector).

Answer 5

Ah, that's what I was trying to do, but it started looking ugly. That was it, though. Thanks for your help!