i am a little confused, i know gradient vector is Fx and Fy (2 variable function and partial derivatives)…I know you have to normalize the gradient vector in order to use it with directional derivative and to do that you do Pythagorean theorem and whatever your answer is you divide your gradient vector to get unit vector for directional derivative….
My question is say you have a 3 variable function (x,y,z) given some point and gradient vector how do you get the unit vector because i dont know if Pythagorean theorem works on 3 variables since you know….the triangle things works for 2 variables only…
so how do you get the unit vector for 3 var functions?
Best Answer
Same way.
In any number of dimensions, you divide a vector $\bf v$ by its length to get a unit vector, and in any finite number of dimensions that means $${(x_1,x_2,\dots,x_n)\over\sqrt{x_1^2+x_2^2+\cdots+x_n^2}}$$