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Given a surface $z=f(x,y)$ we need to find the change in temperature $t(x,y,z)$ in the direction of $(a,b)$ at point $(x_0,y_0)$.

My current way of thinking is finding the tangent plane of $f(x,y)$ at $(x_0,y_0)$ using $h = f(x_0, y_0) + f_x(x_0, y_0) * (x-x_0) + f_y(x_0, y_0) * (y-y_0)$

I then proceed to find the directional vector by doing: $v = (x_0+a, y_0+b,h(x_0+a, y_0+b)) - (x_0, y_0, f(x_0, y_0))$

And normalizing it:

$v = v/||v||$

I then dot the gradient of t with v.

My question is how correct is this and if not where have I gone wrong ?

EDIT:: Fixed a mistake

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    Finding the tangent plane is the right way to go, but you need a unit *vector* in the direction of travel along the surface. You have defined $v$ to be a scalar, so you can't dot $v$ with $\nabla t$.2012-11-12
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    Sorry, I edited the question2012-11-12
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    Does $z=f(x,y)$ represent a constraint on $(x,y)$ or a function?2012-11-12
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    It's a function.2012-11-12
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    Then does my answer address your concern?2012-11-12

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